Question

Find the sum of the first 200 terms of the arithmetic sequence that begins: 12, 18, 24, ...

Answer 1

S₂₀₀ = 121800

Explanation:

the sum to n term 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 = 12 and d = a₂ - a₁ = 18 - 12 = 6 , then

S₂₀₀ =
`(200)/(2)` [ (2 × 12) + (199 × 6) ]

= 100(24 + 1194)

= 100 ×1218

= 121800