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## #1 2017-11-20 08:44:38

samshc
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### Arithmetic Series - Finding the first term when given 2 sums

I'm really struggling with this question.

"The sum of an AP to four terms is 38.
The sum of the same AP to eight terms is 124.
Find the first term and the common difference."

Any help greatly appreciated.

## #2 2017-11-20 09:02:20

zetafunc
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Registered: 2014-05-21
Posts: 2,210
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### Re: Arithmetic Series - Finding the first term when given 2 sums

Suppose that the first term is
, and let the difference between each term be
. The progression is an AP (arithmetic progression), which means that the terms all have a constant difference: a, a + d, a + 2d, a + 3d, ...

The sum of the AP to four terms is 38. This means:

a + (a + d) + (a + 2d) + (a + 3d) = 4a + 6d = 38

Now, how can you use the fact that the sum of the same AP to eight terms is 124, to finish the question?

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