If the sum of the first $100$ $100$ terms of an arithmetic series with common difference $9$ $9$ is $20888$ $20888$ , what is the first term?

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If the sum of the first $100$ $100$ terms of an arithmetic series with common difference $9$ $9$ is $20888$ $20888$ , what is the first term?

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Answer 1 · 2017-04-10T02:09:26

The first term is $- 236.62$ $-236.62$ .

Explanation:

We use the formula $s_{n} = \frac{n}{2} (2 a + (n - 1) d)$ $s_n = n/2(2a + (n - 1)d)$ to find the sum of the first $n$ $n$ terms of an arithmetic series with common difference $d$ $d$ and first term $a$ $a$ .

$20888 = \frac{100}{2} (2 a + (100 - 1) 9)$ $20888 = 100/2(2a + (100 - 1)9)$

Solving for $a$ $a$ we obtain:

$20888 = 50 (2 a + 891)$ $20888 = 50(2a + 891)$

$20888 = 100 a + 44550$ $20888 = 100a + 44550$

$- 23662 = 100 a$ $-23662 = 100a$

$a = - 236.62$ $a = -236.62$

$:.$ The first term of the series is $-236.62$ .

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Explanation:

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