Question

For the arithmetic sequence beginning with the terms {7, 11, 15, 19, 23 ...}, what is the sum of the first 31 terms?

Answer 1

S₃₁ = 2077

Explanation:

the sum to n terms of an arithmetic sequence is

`S_(n)` =
`(n)/(2)` [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = 7 and d = a₂ - a₁ = 11 - 7 = 4 , then

S₃₁ =
`(31)/(2)` [ (2 × 7) + (30 × 4) ]

= 15.5 (14 + 120)

= 15.5 × 134

= 2077