Question

In a G.P., a = 2, T_n = 162 and S_n = 242. Find the value of n.

Answer 1

`S_n = (r(T_n) - a)/(r - 1)`

242 = `(162r - 2)/(r - 1)`

242(r − 1) = 162r − 2

242r − 242 = 162r − 2

80r = 240

r = `240/80`

r = 3

T_n = a . r^{n − 1}

162 = 2 . 3^{n − 1}

81 = 3^{n − 1}

81 = 3⁴

n − 1 = 4

n = 5