Q6 of 110 Page 48

If the geometric sequences 162, 54, 18,…. and ,…have their nth term equal, find the value of n.

Given:For 1^st G.P-

a₁ = 162 and a₂ = 54,

And for 2^nd G.P-

R = 3

∵ a_n = a₁r^n-1 (n = no. of term, a₁ = first term of G.P, r = common ratio)

And ∵ nth term of both G.P are equal,

⇒ a_n = A_n.

⇒ a₁r^n-1 = A₁R^n-1

⇒ n-1 = 4

⇒ n = 5.

In a geometric sequence, the first term is and the sixth term is , find the G.P.

Which term of the geometric sequence,

(i) 5, 2, … , is (ii) 1, 2, 4, 8,…, is 1024 ?

The fifth term of a G.P. is 1875. If the first term is 3, find the common ratio.

The sum of three terms of a geometric sequence is and their product is 1. Find the common ratio and the terms.

Questions · 110

2. Sequences and series of real numbers

1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 1 1 1 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 11 12 1 1 1 1 1 1 2 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20