Question

In an AP., the first term is 32 and the last term is −10. If the common difference is −2, then find the number of terms and their sum.

Answer 1

Given: First term (a) = 32

Last term (l) = −10

Common difference (d) = −2

Formula: a_n = a + (n − 1) d

−10 = 32 (n − 1)−2

−10 = 32 − 2n + 2

−10 = 34 − 2n

−10 − 34 = 2n

−44 = 2n

n = `(-44)/2`

n = 22

`S_n = n/2(a + l)`

= `22/2(32 + (-10))`

= 11(32 + (−10))

= 11 × 22

= 242