Question

The common difference of an ap is -2 find its sum of first term is hundred and last term is -10 with full solution

Answer 1

2520

Explanation:

The n th term of an AP is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference.

To find the number of terms given
`a_(n)` = - 10 , d = - 2 and a₁ = 100, then

100 - 2(n - 1) = - 10 ( subtract 100 from both sides )

- 2(n - 1) = - 110 ( divide both sides by - 2 )

n - 1 = 55 ( add 1 to both sides )

n = 56 ← number of terms

Given n, a₁ and a₅₆ , then the sun of the terms is

`S_(56)` =
`(n)/(2)` (a₁ + a₅₆ )

=
`(56)/(2)` (100 - 10) = 28 × 90 = 2520