Find the sum of the arithmetic sequence. 3, 5, 7, 9, ..., 21

The answer is:120

Given the arithmetic sequence

3, 5, 7, 9, ..., 21

The first term a = 3 & a common difference d = 5 - 3 = 7 - 5 = ... = 2

If there are n number of terms in the above A. P. then last term l = 21 will be the nth term given as:

l = a + (n - 1) d

21 = 3 + (n - 1) 2

n = 10

Hence the sum of given arithmetic progression (A. P.) up to 10 terms is given general formula.

Sn = n/2 (a + l)

S10 = 10/2 (3 + 21)

= 120