Question

an arithmetic series has first term 160 and common difference d . the sum of the first 25 terms of the series 3500 . find the common difference d.

Answer 1

d = -
`(5)/(3)`

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 = 160, n = 25 and
`S_(25)` = 3500 , thus

`(25)/(2)` [ (2 × 160) + 24d ] = 3500, that is

12.5(320 + 24d) = 3500 ( divide both sides by 12.5 )

320 + 24d = 280 ( subtract 320 from both sides )

24d = - 40 ( divide both sides by 24 )

d = -
`(40)/(24)` = -
`(5)/(3)`