The first two terms of an arithmetic progression are 21 and 18.If the sum of the first th term is -24.Find the value of

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- October 11th 2010, 04:32 AMmastermin346Problem Involving Arithmetic progression
The first two terms of an arithmetic progression are 21 and 18.If the sum of the first th term is -24.Find the value of

- October 11th 2010, 04:47 AMemakarov
If you know the the first two terms, you know the initial term and the common difference. This Wikipedia article then gives you the formula for the sum of n terms, so you have to solve the equation for n.

- October 11th 2010, 07:05 AMrtblue
The formula for a sum of a finite arithmetic series is:

In this formula, is the first term. n is the number of terms. d is the common difference (the rate at which the series progresses).

We know that the first term is 21, and we know that the common difference is -3, and that the sum of this series is -24.

Therefore, we have:

now we solve for n:

divide by three to get:

Therefore:

or

or

Since we cant have a negative number of terms, -1 is not a valid answer. Thus, we have :

- October 11th 2010, 07:24 AMArchie Meade