Question

Find the first three terms of the arithmetic series described.

a_1=1,a_n=19,S_n=100

Answer 1

1, 3, 5

Explanation:

The sum of an arithmetic series is:

S_n = n (a_1 + a_n) / 2

100 = n (1 + 19) / 2

n = 10

The nth term of an arithmetic sequence is:

a_n = a_1 + d (n − 1)

19 = 1 + d (10 − 1)

d = 2

The common difference is 2. So the first three terms are 1, 3, and 5.