What is the sum of the arithmetic sequence 8, 15, 22 …, if there are 26 terms?

Solution:\

The sum of ‘n’ terms in an arithmetic progression is:

S_n = (n/2)[2a + (n -1)d]

Given the arithmetic sequence:

8, 15, 22 …

a = first term = 8,

d = common difference = 15 - 8 = 7,

n = 26

⇒ S_n = (n/2)[2a + (n - 1) d]

⇒ S₂₆ = (26/2)[(2 × 8)+(26 - 1)7]

⇒ S₂₆ = 13[16 + 175]

⇒ S₂₆ = 2483

Therefore, the sum of the arithmetic sequence is S₂₆ = 2483.

What is the sum of the arithmetic sequence 8, 15, 22 …, if there are 26 terms?

Summary:

The sum of the arithmetic sequence 8, 15, 22 …, if there are 26 terms, is S₂₆ = 2483.