Question

The 4th term of a G.P is 24 and 8th term is 384.Find the series.

Answer 1

hope this helps you....

Answer 2

Solution :-

Let the G.P. be a, ar, ar².....

Where,

nth term ⇒ Tn = arⁿ⁻¹

T₄ = ar³ = 24..................................(1)

T₈ = ar⁷ = 384................................(2)

Dividing equation (2) by (1)

⇒ ar⁷/ar³ = 384/24

⇒ r⁴ = 16

⇒ r⁴ = 2⁴

⇒ r = 2

So, common ratio is 2

Now, putting the value of r = 2 in (1)

ar³ = 24

⇒ a × 2³ = 24

⇒ 8a = 24

⇒ a = 24/8

⇒ a = 3

So, the first term is 3

The required series is as follows.

3, 3*2, (3*2²), (3*2³), (3*2⁴)

⇒ 3, 6, 12, 24, 48.......

Answer.