Question

For a G.P., if S₅ = 1023, r = 4, find a.

Answer 1

r = 4, S₅ = 1023

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

∴ S₅ = `"a"((4^5 - 1)/(4 - 1))`

∴ 1023 = `"a"((1024 - 1)/3)`

∴ 1023 = `"a"/3(1023)`

∴  a = 3.