Question

Second term of a geometric progression is 6 and its fifth term is 9 times of its third term. Find the geometric progression. Consider that each term of the G.P. is positive.

Answer 1

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

Now, 2^nd term = t₂ = 6 `=>` ar = 6

Also, t₅ = 9 × t₃

`=>` ar⁴ = 9 × ar²

`=>` r² = 9

`=>` r = ±3

Since, each term of a G.P. is positive, we have r = 3 and ar = 6

`=>` a × 3 = 6

`=>` a = 2

∴ G.P. = a, ar, ar², ar³, ........

= 2, 6, 2 × (3)², 2 × (3)³, ............

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