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

##### 1 Answer
Apr 10, 2017

The first term is $- 236.62$.

#### Explanation:

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

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

Solving for $a$ we obtain:

$20888 = 50 \left(2 a + 891\right)$

$20888 = 100 a + 44550$

$- 23662 = 100 a$

$a = - 236.62$

$\therefore$ The first term of the series is $- 236.62$.

Hopefully this helps!