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An arithmetic and a geometric sequence 2021-08-29
Moti pose la question :
Let {an} be an arithmetic sequence such that its 1st, 20th, and 58th terms are consecutive terms of some geometric sequence. Find the common ratio of the geometric sequence.
Harley Weston lui répond.
Loan payment formula 2019-02-24
Kenneth pose la question :

I have a question regarding the loan payment formula shown below.

Calculating the Payment Amount per Period
The formula for calculating the payment amount is shown below.

Simple Amortization Calculation Formula

A = P X r(1 + r)n over (1 + r)n - 1

where

A = payment Amount per period

P = initial Principal (loan amount)
r = interest rate per period

n = total number of payments or periods

Is this formula/calculation a condensed version of a longer calculation? I am curious to know how the (1 +r)n - 1 was developed from the longer calculation. For example, r(1 + r)n may have been (r + rn)n. The n's are exponents.

I thank you for whatever helpful explanation that may be provided.

Kenneth


Harley Weston lui répond.
A geometric series 2018-03-13
nathi pose la question :
Hi I am really struggling with this question please help !!!!
a pohutukawa tree is 86 centimetres when it is planted. in the first year after it is planted , the tree grows 42 centimetres in height.Each year the tree grows in height by 95% of the growth of the previous year.
assume that the growth in height of the pohutukawa tree can be modelled by a geometric sequence.
A)find the height of the tree 5 years after it is planted and figure out the maximum height the pohutukawa tree is expected to reach in centimetres. The maximum height part is not answered.

Penny Nom lui répond.
Triakis 2016-06-27
Gordon pose la question :
Some authorities treat "triakis" (and related terms "dyakis", "tetrakis", etc.) as attached prefixes; others treat them as separate adjectives. Thus I see one of the Catalan solids described as both "triakistetrahedron" and "triakis tetrahedron". Which usage is correct?
Chris Fisher lui répond.
A geometric progression 2016-03-03
Pauline pose la question :
A woman measures the height of her child at birth and at monthly intervals afterwards.The child's height increases by 5% per month. Find the number of measurements she has made before the child's height is twice what it was at birth
Penny Nom lui répond.
A geometric sequence 2015-04-19
Delfina pose la question :
In a geometric sequence the second term is 15 and the fifth term is -405. Find the sum of the first eight terms
Penny Nom lui répond.
Find the nth term 2014-10-26
Kenneth pose la question :
According to the pattern of the following sequence. Find it's nth term: 3,9,27,81,243,..........
Penny Nom lui répond.
9,-4,6,-8,3,... 2014-03-31
Alynna pose la question :
You are given the following pattern: 9,-4,6,-8,3,...
Create a formula for the nth figure.

I have trouble finding the formula, I need help trying to find it.

Penny Nom lui répond.
An infinite geometric series 2013-12-24
Muhammad pose la question :
The sum of an infinite geometric series is 15 and the sum of their squares is 45. Find the series
Penny Nom lui répond.
A geometric sequence 2013-07-16
Relebohile pose la question :
Find the n^th term of 3,6,9,12,24,48...
Penny Nom lui répond.
A geometric sequence 2012-06-10
vicki pose la question :
The sum of the first three terms of a geometric sequence of positive integers is equal to seven times the first term, and the sum of the first four terms is forty-five. What is the first term of the sequence?
Penny Nom lui répond.
A geometric sequence 2012-02-24
Camille pose la question :
Find x if the sequence 5,10,x+2 is geometric.
Penny Nom lui répond.
A tree growth modelled by a geometric series 2012-02-08
Steph pose la question :
Hi I am really struggling with this question please help !!!!
a pohutukawa tree is 86 centimetres when it is planted. in the first year after it is planted , the tree grows 42 centimetres in height.Each year the tree grows in height by 95% of the growth of the previous year. assume that the growth in height of the pohutukawa tree can be modelled by a geometric sequence.
A)find the height of the tree 5 years after it is planted and figure out the maximum height the pohutukawa tree is expected to reach in centimetres

Penny Nom lui répond.
1 + 3 + 3^2 ...+3^(n-1) = 3^n - 1/2 2012-01-27
Vicki pose la question :
I am trying to find out how to do show how this proof was worked.
Here is the end result 1 + 3 + 3^2 ...+3^(n-1) = 3^n - 1/2

This equation was used to find the number of white triangles in the Sierpinski Triangle

Walter Whiteley lui répond.
Mean and Average 2012-01-03
john pose la question :
what is the difference between average and mean
Robert Dawson lui répond.
An imaginary infinite geometric tree 2011-02-18
Elise pose la question :
An imaginary infinite geometric tree grows 1m the first day. 2nd day 2 branches and right angles to each other and each 0.5 m long. 3rd day two new branches at ends of each of previous days' 2 branches, again at right angles, and only .25m long each.
And so on, infinitely.
Q: Use relationships of right-angled triangles and high school level knowledge of geometric series to show the tree height is limited to (4 + sqrt2)/3 m and width to (2(sqrt2 + 1))/3 m.

Robert Dawson lui répond.
A geometric progression 2010-12-15
Abeth pose la question :
find the value of x so that 2(x-1), x+3, x will be a geometric progression.
Penny Nom lui répond.
The value after 30 years 2010-12-15
Abeth pose la question :
At the end of every year, the owners of a building which costs 2, 500, 000 pesos deducts 15% from its carrying value as estimated at the beginning of the year. find the estimated value at the end of 30 years.
Penny Nom lui répond.
A geometric progression 2010-04-30
Kalyani pose la question :
sum of infinite geometric progression is 9 and common ratio is 1/10 then sum up to 8 terms is?
Chris Fisher lui répond.
A geometric sequence 2010-04-13
glen pose la question :
A geometric sequence has a first term of 0.1024, a second term of 0.256, and a middle term of 156.25. how many terms are there in the whole sequence? i know that r=2.5 but i dont know how to find how many terms there are.
Penny Nom lui répond.
A geometric sequence 2010-02-22
Kelsey pose la question :
_, 2, _, _, 250, _

i don't know how to fill in the missing terms

Penny Nom lui répond.
An infinite geometric series 2009-05-18
terri pose la question :
find the sum of the infinite geometric series

14 -7 +7/2 -7/4 +.....

A. 7007/13 B. 2002 C. 28/3 D.5005/7

Stephen La Rocque lui répond.
A geometric progression 2009-05-16
sweta pose la question :
find the ratio of GP if the first term is 1 and the sum of third and fifth term is 90.
Penny Nom lui répond.
A geometric construction 2008-10-17
M pose la question :
Given any 3 parallel lines on a plane, how to construct an equilateral triangle with each vertex on each line?
Chris Fisher lui répond.
0.151515...=15/99 2008-09-08
Emma pose la question :
This week, my Algebra teacher told us about the pattern between infinitely repeating decimals and their corresponding fractions. (ex. .2222222...= 2/9, .151515...=15/99, 456456456...=456/999, etc.) I was just wondering the reason why this pattern occurs. Is there a certain element that causes this pattern to occur?
Thanks
-Emma

Penny Nom lui répond.
Proofs 2008-07-26
Taylor pose la question :
when doing a proof, how do i figure out the steps in which i find the statements? i find the reasons pretty easily but i do not understand how to get the proving part. that would be great if you can help me! Thanks
Victoria West lui répond.
Demographics 2008-07-25
shahrukh pose la question :
Each year for 10 years ,the population of a city increased by 5% of its value in the previous year. If the initial population was 200 000 ,what was the population after 10 years ??
Penny Nom lui répond.
Geometric shapes that are the same 2008-06-09
tia pose la question :
what is the name used for shapes that are exactly the same?
Harley Weston lui répond.
Geometric sequences 2008-06-08
Rita pose la question :
A geometric sequence is given. Find the common ratio and write out the first four terms.

(1) {(-5)^n}

(2) {(2^n)/(3^(n - 1)}

Penny Nom lui répond.
A parallel line to a given line 2008-04-12
john pose la question :
A parallel line to a given line through a given point not on the a given line
Harley Weston lui répond.
The nth term 2007-10-18
shannon pose la question :
Ok , what i am having problems with is the nth term. I get how the numbers come together, but i am having trouble with finding the nth term.
Penny Nom lui répond.
Finding a geometric mean and taking its antilog 2007-08-27
Jack pose la question :
Would like to know the basic geometric mean calculation. Also how would I take the antilog from this number?
Stephen La Rocque lui répond.
Applications of sequences and series 2007-08-27
Trish pose la question :
I'm a grade 12 learner working on a math project based on sequences and series. I'd like to know the different types of sequences and series such as fibonacci, fourier, farey, etc.

I've already used the Fibonacci Sequence and Harmonic Series and need two more. The simpler the sequence or series type the better.

I'd also like to know in which non-mathematical areas use sequences and series and how. Areas such as engineering or science.

Penny Nom lui répond.
A sequence of circles 2007-06-11
Ann pose la question :
Please help with solving the following problem!!! A circle is inscribed in an equilateral triangle with a side of length 2. Three circles are drawn externally tangent to this circle and internally tangent to 2 sides of the triangle. 3 more circles are drawn externally tantgent to these circles and internally tangent to 2 sides of the triangle. if this process continued forever, what would be the sum of the areas of all the circle? the answer 1 parent came up with was Pie over 2, but we don't know how he did it. Can you please show the work or explain the answer to this problem? Thank you Ann p s my daughter is in 9th grade math.
Steve La Rocque, Chris Fisher and Penny Nom lui répond.
Arithmetic means and geometric means 2007-04-04
Dani pose la question :
Hi! I was just wondering why the arithmetic mean of sets of numbers is larger than the mean proportional of the same numbers? Thanks! Dani
Haley Ess lui répond.
A geometric series 2007-04-03
jessica pose la question :
If a geometric series includes 54-18+6-2 as its fifteenth through eighteenth terms, find the sum of the second through the fifth term, inclusive.
Stephen La Rocque lui répond.
The nth term 2007-02-13
Sarah pose la question :
I am having difficulty in finding the nth term for 7,49,343,2401. Could you please help me in finding the correct answer?
Stephen La Rocque lui répond.
Find the total distance the swing traveled before it stopped. 2006-12-17
Leah pose la question :
Rebecca's little sister liked for her to push her in the swing at the park. The other day Rebecca pulled the swing back and let it go. She would have kept pushing, but she suddenly saw a friend at the other end of the park. The swing traveled a total distance of 10 feet before heading back the other way. Each swing afterwards was only 80% as long as the previous one. Find the total distance the swing traveled before it stopped.
Penny Nom lui répond.
A geometric sequence 2006-11-28
Jillian pose la question :
Find x so that 2x, x + 5, x - 7 are consecutive terms of a geometric sequence.
Stephen La Rocque lui répond.
Geometric sequence and basic functions (graphs) 2006-04-20
Marlene pose la question :
Which of the basic functions is related to the geometric sequence: Linear, Quadratic, Rational, or Exponential? Can you give me an example of how it would be used in normal life?
Stephen La Rocque lui répond.
Arithmetic and Geometric Sequences 2006-04-19
Skye pose la question :
If the 1st, 4th, and 8th terms of an arithmetic sequence are consecutive terms in a geometric sequence, find the common ratio of the geometric sequence.
Stephen La Rocque lui répond.
Sum of a Geometric Sequence 2006-04-11
Andre pose la question :
In a particular geometric sequence, U3=-3.6 and U10=12.9. Find S16 and S17.
Stephen La Rocque lui répond.
An isosceles triangle 2005-11-14
Chris pose la question :
PX and QY are attitudes of acute triangle PQR, and Z is the midpoint of PQ. Can you write a proof that triangle XYZ is isosceles?
Chri Fisher lui répond.
A geometric sequence 2005-06-21
A student pose la question :

The first three terms of a geometric series are 3(q+5), 3(q+3), (q+7) respectively.
Calulate the value of q.


Penny Nom lui répond.
A geometric proof 2004-12-11
Hanna pose la question :
Given: ABCD is a quadrilateral;
Prove: ABCD is a parallelogram

Penny Nom lui répond.
Geometric sequence 2004-12-04
Lesa pose la question :
Find a formula for the geometric sequence: (√3 - √2), (4 - √6), (6√3 - 2√2), …
Penny Nom lui répond.
A geometric sequence 2004-04-13
Michael pose la question :
In a geometric series, the sum of the 2nd and 3rd terms is 60, and the sum of the 3rd and 4th terms is 240. Find the sum of the first 7 terms.
Penny Nom lui répond.
A worm crawling home 2004-02-18
Cindy pose la question :
A worm is crawling to his home which is one meter away. The longer he crawls the weaker he gets and the less he can crawl the next day. If he crawls within 1/3000 of a meter of his home, he will find food. He must eat within twelve days. The first day he crawls 1/2 meter. The second day he crawls 1/4 meter. The third day he crawls 1/8 of meter. This pattern continues for twelve days. Make a Chart that shows the distance he has covered at the end of each day and the total he has covered at the end of each day. Does he make it to the Food in time?
Penny Nom lui répond.
Geometric sequences 2004-02-03
Alan pose la question :
hello, I am a junior in precalculus. we started working on geometric sequences today, it makes perfect sense on how it works. but why is it called that? if you could send me an answer to why geometric sequences have that name, I would be much appreciative.
Chris Fisher lui répond.
8 faces, 12 vertices, and 18 edges 2003-04-22
Thomas pose la question :
I would like to know the proper name for this geometrical solid. It has 8 faces, 12 vertices, and 18 edges?
Penny Nom lui répond.
A bouncing ball 2002-12-14
Eman pose la question :

Q : When a childís ball is dropped from a height h metres on to a hard, flat floor, it rebounds to a height of 3/5h metres. The ball is dropped initially from a height of 1.2m.

  1. Find the maximum height to which the ball rises after two bounces.
  2. Find the total distance that the ball has traveled when it hits the floor for the tenth time.
  3. Assuming that the ball continues to bounce in the same way indefinitely, find the total distance that the ball travels.

Penny Nom lui répond.
A geometric sequence 2002-12-02
Wanda pose la question :
the fifth term of a geometric sequence is 5/16. the common ratio is 1/2. What are the first four terms of the sequence.
Penny Nom lui répond.
My salary is doubled everyday for 30 days 2002-01-17
Kanishk pose la question :
I recieve 1 penny the 1st day, 2 pennies the 2nd day, and my salary is doubled everyday for 30 days. How much money will I have by the end of the 30 day time period? (Is there a way of solving this problem without a chart?)
Penny Nom lui répond.
A geometric series 2001-10-24
Tashalee pose la question :
The sum of the first 3 terms of a geometric series is 13. The sum of their reciprocal is 13/9. how do you find the first three terms?
Penny Nom lui répond.
The average of two polygons 2001-10-23
Irene pose la question :
How can I prove that the average of two polygons will give me another one?
Walter Whiteley lui répond.
Geometric and arithmetic sequences 2001-01-26
Garry pose la question :
what are the equations for geometric and arithmetic sequences?

also, what are the equations for finding the sums of those series?


Leeanne Boehm and Penny Nom lui répond.
Power series representations 2000-11-27
Grace pose la question :
Is there a systematic way of finding a power series representation of a function? I understand that you have to manipulate the function so that it is of the form 1/(1-x), but beyond that I am lost.
Harley Weston lui répond.
Comparing an integral and a sum 2000-11-21
Douglas Norberg pose la question :
A fellow teacher asked me about a problem she wanted to give to her students. It involved whether to take a million dollars or a penny doubled a number of times. I was able to determine the number must have been .01 * 230 which is about $10 million and a lot more than $1 million. To check that I was right I used a spreadsheet and did a Riemann sum.

When I finished I reasoned that I had done the task in several steps and I could have done it in 1 step. Thus I integrated .01 * 2x from 0 through 30 but the number I got was $15,490,820.0324. Why the difference?


Harley Weston lui répond.
Infinite Geometric Series 2000-11-10
Sam Carter pose la question :
I ran into a problem when studying how to find the sum of an infinite geometric series. My math book attempts to explain the concept by giving formulas involving sigma and |r|, but it does not really explain how to go about finding the sum of an infinite geometric series. If you could either help me with this or point me in the direction of an informative website that could help me, I'd appreciate it.
Harley Weston lui répond.
Geometric sequences 2000-04-11
Jodie pose la question :
I am in a grade ten principles class and was taught how to do geometric sequences and series but no one in my class understood what we were taught. Our teacher is one of few to use the new curriculum which used to be the grade twelve curriculum. Could you please explain to me how to do geometric sequences and how to find the different terms and sums. Thank you very much!
Harley Weston lui répond.
Geometrical solids 2000-03-15
Sarah pose la question :
  1. What geometrical solid has 8 edges and 5 vertices?
  2. What geometrical solid has 12 edges that are all the same length?

Walter Whiteley lui répond.
Pyramids and prisms 2000-01-18
Tyler pose la question :
What's the definition of a Triangular Prism and a Triangular pyramid.
Penny Nom lui répond.
Dotted graph paper 1999-04-08
Bridget Winward pose la question :
A teacher at our school is trying to locate dotted graph paper online or in print. His class would like to make three dimensional, geometerical drawings.
Please let us know if you have a good source.

Jack LeSage lui répond.
Two sides and a bisectrix. 1998-11-11
Victor Grinshtein pose la question :
I am looking for someone who can tell me how to construct a triangle by 2 sides and a bisectrix using a compass and a ruler.
Chris Fisher lui répond.
A Pattern 1998-09-14
Krystin pose la question :
Question:
1=1x1
1+2+1=2x2
1+2+3+2+1=3x3

draw a series of diagrams to illustrate the above pattern
Penny Nom lui répond.

Sequences and series 1998-05-27
Michael Le Francois pose la question :
The sum of the first ten terms of an arithmetic series is 100 and the first term is 1. Find the 10th term.

The common ratio in a certain geometric sequence is r=0.2 and the sum of the first four terms is 1248 find the first term.
Penny Nom lui répond.

 
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