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

An arithmetic progression is a sequence where the differences between every two consecutive terms are the same.

## Answer: The sum of the arithmetic sequence is 120.

Let's observe the pattern and get the sum of the arithmetic sequence.

## Explanation:

Given arithmetic sequence: 3, 5, 7, 9, ..., 21

The first term of the sequence is a = 3 and a common difference is d = 5 − 3 = 2

If there are n number of terms in the above arithmetic sequence, then last term a_{n }= 21 will be taken as the nth term that is given as

a_{n }= a + (n − 1) d

21 = 3 + (n − 1) 2

2 (n - 1) = 18

n - 1 = 9

n = 10

hence the formula for sum of given arithmetic progression up to 10 terms is given as

S_{n }=n/2 (a_{1 }+ a_{n})

S_{10 }= 10/2 (3 + 21)

S_{10 }= 120

Hence, the sum of the arithmetic sequence 3, 5, 7, 9, ..., 21 is 120.