Sequences Help

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sparkle6: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Tue Sep 20, 2011 7:58 amFollowed by: 1 member; Thanked: 1 times

by sparkle6 » Mon Nov 14, 2011 2:53 am

Can anyone provide me with the sequence formula for finding a particular term in a sequence?

I'm aware that the formula for the sum of a sequence is:
(number of terms) * (average of the first and last term)

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Source: Beat The GMAT — Problem Solving | Mon Nov 14, 2011 2:53 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Nov 14, 2011 3:08 am

sparkle6 wrote:Can anyone provide me with the sequence formula for finding a particular term in a sequence?

I'm aware that the formula for the sum of a sequence is:
(number of terms) * (average of the first and last term)

Say the sequence is 8, 17, 26, 35... and we need to find the 10th term of this sequence.

nth term of an arithmetic sequence is given by a(n) = a(1) + (n - 1)d, where a(n) -> nth term, a(1) -> first term, d -> common difference, n -> no. of terms

Now in the sequence given a(1) = 8, d = 35 - 26 = 26 - 17 = 17 - 8 = 9, n = 10, since we have to find the 10th term.
So, a(10) = 8 + (10 - 1)9 = 8 + (9 * 9) = 8 + 81 = 89

Hope that helps.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Nov 14, 2011 6:31 am

sparkle6 wrote:Can anyone provide me with the sequence formula for finding a particular term in a sequence?

I'm aware that the formula for the sum of a sequence is:
(number of terms) * (average of the first and last term)

I received a PM asking me to comment.
I don't really have much to add beyond Anurag's post, but here's my approach:

An arithmetic sequence is a set of evenly spaced integers.
To determine the value of a specific term in an arithmetic sequence, just ask yourself how many times the value of d -- the distance between successive terms -- must be added to the 1st term:

For the 2nd term, the value of d must be added to the 1st term 1 time.
For the 3rd term, the value of d must be added to the 1st term 2 times.
For the 100th term, the value of d must be added to the 1st term 99 times.
In other words, for the nth term, the value of d must be added to the 1st term n-1 times.

Put into a formula:
The nth term = the 1st term + (n-1)d.

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Mon Nov 14, 2011 7:27 am

sparkle6 wrote:Can anyone provide me with the sequence formula for finding a particular term in a sequence?

I'm aware that the formula for the sum of a sequence is:
(number of terms) * (average of the first and last term)

Here is it -

where

a = First term of the series

n = No of terms of the series

d = Common difference between the terms

Abhishek

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