Question

Find the number of terms in the ap if (x+y)+(x-y)+(x-3y)+....... =22 (x-20y)
Pls do answer..... I am not able to do this

Answer 1

Answer:

(x + y) + (x - y) +(x - 3y) =22(x - 20y)

a = x+y , d = -2y , Sn = 22(x- 20y)

⇒ n/2(2a +(n -1)d) = 22(x - 20y)

⇒ n/2(2x + 2y + (n -1)(-2y)) = 22x - 440y

⇒ n(x + y - ny + y) = 22(x - 20y)

⇒ nx + n(-n + 2) y = 22(x - 20y)

Comparing on both sides we get

∴n = 22.