Question

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

Answer 1

#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=n/2[2a+(n-1)d]`

`therefore S_120=102/2[(2)(5)+(120-1)(7)]`

`=42993`.