Question

For a G.P., if a = 2, r = `-2/3`, find S₆.

Answer 1

a = 2, r = `-2/3`

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

∴ S₆ = `(2[1 - (-2/3)^6])/(1 - (-2/3)`

= `(2[1 - (-2/3)^6])/(5/3)`

= `6/5[(729 - 64)/3^6]`

= `6/5[665/729]`

∴ S₆ =  `266/243`.