Question

Find the sum of the first 49 terms of the arithmetic series. 36+42+48 +54 + ... S49 =

Answer 1

S₄₉ = 8820

Explanation:

the sum to n terms of an arithmetic series is

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

where a₁ is the first term and d the common difference

here a₁ = 36 and d = a₂ - a₁ = 42 - 36 = 6 , then

S₄₉ =
`(49)/(2)` [ (2 × 36) + (48 × 6) ]

= 24.5 (72 + 288)

= 24.5 × 360

= 8820