Question

Find the sum of the first 50 terms of the arithmetic sequence

with first term 6 and common difference 1/2
.

Answer 1

S₅₀ = 912.5

Explanation:

the sum of 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 = 6 and d =
`(1)/(2)` , then

S₅₀ =
`(50)/(2)` [ (2 × 6) + (49 ×
`(1)/(2)`) ]

= 25(12 + 24.5)

= 25 × 36.5

= 912.5