Question

Find the geometric progression with 4^th term = 54 and 7^th term = 1458.

Answer 1

Let the first term of the G.P. be a and its common ratio be r.

4^th term = 54 `=>` ar³ = 54

7^th term = 1458 `=>` ar⁶ = 1458

Now, `(ar^6)/(ar^3) = 1458/54`

`=>` r³ = 27

`=>` r = 3

ar³ = 54

`=>` a × (3)³ = 54

`=> a = 54/27 = 2`

∴ G.P. = a, ar, ar², ar³, ........

= 2, 2 × 3, 2 × (3)², 54, ...........

= 2, 6, 18, 54, ............