# 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?

Mar 28, 2016

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