Question

Here is an arithmetic series: 7 10 13 16 ... 154. a, = 7 and a50 = 154. find the sum of the first 50 terms of the sequence.

Answer 1

S₅₀ = 4025

Explanation:

the sum to n terms of an arithmetic series is

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

a₁ is the first term , d the common difference, n the term number

to find S₅₀ we require to find the common difference d

the nth term of an arithmetic series is

`a_(n)` = a₁ + (n - 1)d

given a₁ = 7 and a₅₀ = 154 , then

7 + 49d = 154 ( subtract 7 from both sides )

49d = 147 ( divide both sides by 49 )

d = 3

Then

S₅₀ =
`(50)/(2)` [ (2 × 7) + (49 × 3) ] = 25(14 + 147) = 25 × 161 = 4025