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 (a₁ + a_n)

S₁₀ = 10/2 (3 + 21)

S₁₀ = 120

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

Thus, the sum of the arithmetic sequence is 120.