Question

For a G.P., if a = 2, r = 3, S_n = 242, find n.

Answer 1

a = 2, r = 3, S_n = 242

S_n = `"a"(("r"^"n" - 1)/("r" - 1))`, for r > 1

∴ 242 = `2((3^"n" - 1)/(3 - 1))`

∴ 242 = 3ⁿ – 1
∴ 3ⁿ = 243
∴ 3ⁿ = 3⁵
∴ n = 5.