Find the geometric progression whose 4th term is 54 and the 7th term is 1458.

Given, a 4 = 54 and a 7 = 1458. By formula, a n = ar n - 1 . ⇒ a 4 = a(r) 4 - 1 ⇒ 54 = ar 3 (Eq 1) ⇒ a 7 = a(r) 7 - 1 ⇒ 1458 = a(r) 6 (Eq 2) Dividing Eq 2 by Eq 1, Putting value of r in Eq 1, a 2 = ar = 2 × 3 = 6 a 3 = ar 2 = 2(3) 2 = 2 × 9 = 18 a 4 = ar 3 = 2(3) 3 = 2 × 27 = 54. Hence, the required G.P. is 2, 6, 18, 54, ...