Question

The first term of an Arithmetic progression is 13 and the 11th term is 83.Find the

common difference and the sum of the first twenty terms.

Answer 1

Below in bold.

Explanation:

First term a1 = 13

11th term a11 = a1 + 10d = 83

So a1 + 10d - a1 = 83 - 13

10d = 70

d = 10

The common difference d = 7.

Sum of n terms = (n/2)[2a1 + (n - 1)d]

Sum of the first 20 terms:

S20 = (20/2)[2*13 + (20-1)7]

S20 = 10 *(26 + 19*7)

S20 = 10*159 = 1590.