SOLUTION: Find the sum of the first 20 terms in the arithmetic series 15 + 4 - 7 - ...

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Question 1035866: Find the sum of the first 20 terms in the arithmetic series 15 + 4 - 7 - ...
Answer by ikleyn(52781) About Me  (Show Source):
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Find the sum of the first 20 terms in the arithmetic series 15 + 4 - 7 - ...
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Use the formula for the sum of the first n terms of an arithmetic progression

S%5Bn%5D =  a%5B1%5D+%2B+a%5B2%5D+%2B+a%5B3%5D+%2B+ellipsis+%2B+a%5Bn%5D = %28a%5B1%5D+%2B+%28n-1%29%2Ad%2F2%29%2An

where a%5B1%5D is the first term, d is the common difference and n is the number of terms (see the lesson Arithmetic progressions in this site).

In your case a%5B1%5D = 15, d = -11, n = 20.

Plug in this data in the formula and get

S%5B20%5D = %2815+%2B+%2819%2A%28-11%29%29%2F2%29%2A20.

Make calculations.