Question

For the arithmetic sequence beginning with the terms {-1, 2, 5, 8, 11, 14...}, what is the sum of the first 16 terms?

Answer 1

S₁₆ = 344

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 = - 1 and d = a₂ - a₁ = 2 - (- 1) = 2 + 1 = 3 , then

S₁₆ =
`(16)/(2)` [ (2 × - 1) + (15 × 3) ]

= 8 (- 2 + 45)

= 8 × 43

= 344