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arithmetic progression

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1 + 2 + 3 + ... + (2n - 1) 2015-01-01
Brian pose la question :
Hi Maths Central
My wife presented me with a query which may have a simple answer, but one that I can’t deduce or explain.

Take the string of numbers, n=1,2,3,4,5…
It seems that n(2n-1) = Sum((1…..(2n-1))
e.g. for n=5, both 5 x 9 and Sum(1….9) equal 45, and so on for other values of n.

Could you please provide an explanation? Does it have an underlying reason and a name?

Look forward to your response.
Brian

Penny Nom lui répond.
An arithmetic progression 2014-11-19
Gbenga pose la question :
In an A.P the difference between 8th and 4th term is 20. The 8th term is 1\2 times the 4th term . Find arithmetic progression..
Penny Nom lui répond.
The sum of the first 50 terms of an arithmetic progression 2014-07-26
Joshua pose la question :
Hello ...my is Joshua...I'm a grade 11 student...I got a question

Calculate the sum of the first 50 terms of an arithmetic progression: 112:98:84

Penny Nom lui répond.
An arithmetic progression 2014-03-31
Japheth pose la question :
The 3rd term of an A.P is 10 more than the first term while the fifth term is 15 more than the second term. Find the first term?
Penny Nom lui répond.
An arithmetic sequence 2014-01-06
paris pose la question :
find the twenty-fifth term of an arithmetic sequence whose first term is 12 and whose common difference is -6
Penny Nom lui répond.
An Arithmetic Progression 2013-10-08
collins pose la question :
In an A.P. the difference between the 8th and 4th term is 20 and the 8th is one and half times the 4th term... what is the common difference and the first term
Penny Nom lui répond.
The sum of all whole numbers from 1 to X 2013-09-06
Tim pose la question :
How do I develop a rule for the sum of all whole numbers from 1 to X when I have no idea how to do this
Penny Nom lui répond.
An arithmetic progression 2013-07-06
ashok pose la question :
the 4th and 10th term a.p respectively 7 and 19 find its 15th term.....
Penny Nom lui répond.
An arithmetic progression 2013-02-06
loberto pose la question :
the 3rd term of an a.p is 10more than the 1st term,while the 5th term is 15more than the 2nd term,find the sum of the 8th and 15th terms of the a.p if the 7th term is 7times the 1st term
Penny Nom lui répond.
An arithmetic progression 2012-08-22
A student pose la question :
the 3rd term of an A.PPP is 10 more than the first term while the 5th term is 15 more than the second.find the sum of the 8th and 15th terms if the 7th term is 7 times the first term.
Penny Nom lui répond.
The 3rd term of an A.P is 10 more than the first term 2011-11-29
Olaniyan pose la question :
the 3rd term of an A.P is 10 more than the first term while the fifth term is 15 more than the second term. Find the sum of the 8th and 15th terms of the A.P if the if the 7th term is 7 times the first term.
Penny Nom lui répond.
4 + 10 + · · · + (6n − 2) 2010-04-21
Lan pose la question :
Find the sum 4 + 10 + · · · + (6n − 2). The answer is 3(n^2) + n. How?
Penny Nom lui répond.
Arithmetic progressions 2006-01-31
A student pose la question :
1)the sum to n terms of a particular series is given by Sn=17n-3n2

a)find an expression for the n term of the series
b)show that the series is an arithmetic progression

2)a particular arithmetic progression has a positive common difference and is such that for any three adjacent terms ,three times the sum of their squares exceeds the square of their sum is 375.Find the common difference


Penny Nom lui répond.
Three prime numbers p,q and r, all greater than 3, form an arithmetic progression: 2005-07-18
Ladis pose la question :
Three prime numbers p,q and r, all greater than 3, form an arithmetic progression: p=p, q=p+d and r= p+2d. Prove that d is divisible by 6.
Chris Fisher lui répond.
An arithmetic progression 2004-12-24
A student pose la question :
the 4th and 5th term of an arithmetic progration 47 and 52 respactively find
a)d
b)a1
c)a50

Penny Nom lui répond.
1+3+5+...+(2n+1) 2004-09-10
Emma pose la question :
Prove that 1+3+5+...+(2n+1)= (n+1)2
Penny Nom lui répond.
The sum of some positive integers 2004-06-07
A student pose la question :
Find the sum of all positive integers not greater than 10000 that are divisible by neither 3 nor 7.
Penny Nom lui répond.
7+8+9+...+1000 2002-09-11
Shirley pose la question :
My question is what is the formula for adding up numbers when you don't start with number 1? For example 3 + 4 + 5 + 6 = 18. But how could you arrive at the answer without adding all the numbers?
Penny Nom lui répond.
Arithmetic progressions 2002-04-24
David pose la question :
I have been searching everywhere for the formula to mathamatical progression.
Penny Nom lui répond.
Arithmetic sequences 2001-09-10
Rachel pose la question :
I can't seem to figure out a problem that deals with arithmetic sequencing. This is the question: The 5th term in an arithmetic sequence is 1/2, and the 20th term is 7/8. Find the first three terms of the sequence. I attempted this problem with the formula: An = a + (n-1)d (where the n represents the nth term, a is the first term, and d represents the common difference) I keep getting -9.5 for the first number, and then 3/120 as the common difference between the numbers. But as I have figured it, the sequence is getting greater and greater, and my data does not go with the terms given.
Penny Nom lui répond.
Arithmetic Progressions 1998-11-12
Gerry Boser pose la question :
It has been years since I was in school and I can't remember if there is a formula for the following problem:

If you deposit $1.00 on the first day of the month, $2.00 on the second day, $3.00 on the third day . . $31.00 on the last day of the month, how much do you have in the bank?

Now will this formula also work if it was, $0.25 (then day two you would deposit 2x $0.25 or $0.50, day three you would deposit 3x $0.25, $0.75. . . ). Will it work with any denomination??

Thank you for your time. I promise I'll write this one down for future reference. . .
Penny Nom lui répond.

Dividing a Class 1998-10-01
Tom Barker pose la question :
My eighth grade niece called with the following homework problem:

A teacher wanted to divide her class into equally numbered groups. She tried to divide the class into groups of two, but was one student short. She tried to divide the class into groups of five, but was one student short. She tried to divide the class into groups of seven and was successful. What is the least number of students that were in her class?

I know the answer is 49, but don't know how to prove it. I must be getting old if I can't solve eighth grade math problems. Your assistance would be appreciated.
Penny Nom lui répond.

 
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