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

Answer:

2520

Step-by-step 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

$S_{56}$ = $\frac{n}{2}$ (a₁ + a₅₆ )

      = $\frac{56}{2}$ (100 - 10) = 28 × 90 = 2520