Question

find the G.P whose 4th term is 54 and 7th term is 1458.​

Answer 1

4th term = 54

7th term = 1458

t₄ = 54

a r³ = 54 ----- (1)

t₇ = 1458

a r⁶ = 1458 ----- (2)

(2)/(1) = (a r⁶)/(a r³) = 1458/54

r³ = 27

r³ = 3³

r = 3

Substitute r = 3 in the first equation we get

a (3)³ = 54

a(27) = 54

a = 54/27

a = 2

The general form of G.P is a, a r , ar², ....

= 2 ,2(3),2(3)²,..............

= 2,6,18,............