# How do you find the sum of the arithmetic sequence having the data given a_1=5, d = 7, n = 120?

Feb 14, 2016

S_120=sum_(n=1)^120 [5+(n-1)(7)] =5+12+19+26+......+838=42993

#### Explanation:

The formula for the sum to $n$ terms of an arithmetic sequence with first terms $a$ and common difference $d$ is given by

${S}_{n} = \frac{n}{2} \left[2 a + \left(n - 1\right) d\right]$

$\therefore {S}_{120} = \frac{102}{2} \left[\left(2\right) \left(5\right) + \left(120 - 1\right) \left(7\right)\right]$

$= 42993$.