Q10 of 176 Page 21

The seventh term of a G.P. is 8 times the fourth term and 5th term is 48. Find the G.P.

T_n = ar^n-1

In the GP, the 7th term is 8 times the 4th term. So

ar⁶ = 8ar³, or

r³ = 8 or r = 2.

ar⁴ = 48,

a.16 = 48

a = 3

The first term is 3 and r = 2

∴ GP = 3, 6, 12, …

Find the 4th term from the end of the G.P.

The fourth term of a G.P. is 27, and the 7th term is 729, find the G.P.

If the G.P.’s 5, 10, 20, …. And 1280, 640, 320, … have their nth terms equal, find the value of n.

If 5^th, 8^th and 11^th terms of a G.P. are p, q and s respectively, prove that a² = ps.