Question

Find the sum of the first 36 terms of the following series, to the nearest integer.

7, 12, 17,...

Answer 1

S₃₆ = 3402

Explanation:

there is a common difference between term in the sequence , that is

12 - 7 = 17 - 12 = 5

this indicates the sequence is arithmetic with sum to n terms

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

where a₁ is the first term and d the common difference

here a₁ = 7 and d = 5 , then

S₃₆ =
`(36)/(2)` [ (2 × 7) + (35 × 5) ]

= 18( 14 + 175)

= 18 × 189

= 3402