# An arithmetic series has a common difference of 7. Given that the sum of the first 20 terms of the series is 530, how do you find the first term of the series?

##### 1 Answer
Mar 28, 2016

$- 5$

#### Explanation:

With the first term as a and common difference d, the sum for n terms = $n a + \frac{n \left(n - 1\right)}{2} d$, using 1 + 2 + 3 +..(n-1) = (n-1)(n)/2
Here, n = 20 and d = 7.

20a + ((19)(20)/2)7 = 530

$20 a = - 100$. So, a = $- 5$.