Question

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

Answer 1

t₄ = ar³ = 54             ...(i) 

t₇ = ar⁶ = 1458          ...(ii)

∴ Dividing (ii) by (i), we get

\(\frac{t_7}{t_4}\) = r³ = \(\frac{1458}{54}\) = 27

⇒ r = 3

∴ From (i), a.(3)³ = 54 

⇒ 27a = 54 

⇒ a = 2

∴ The G.P. is 2, 2 x 3, 2 x 3², ..... , i.e. 2, 6, 18, 54, .... .