Question

Find the next three terms of the following sequence.

8, 24, 72, …

Answer 1

8, 24, 72, …

In an arithmetic sequence a = 8,

d = t₂ – t₁ = t₃ – t₂

= 24 – 8 = 72 – 24

= 16 ≠ 48

So, it is not an arithmetic sequence. In a geometric sequence,

r = `("t"_2)/("t"_1) = ("t"_3)/("t"_2)`

⇒ `24/8 = 72/24`

⇒ 3 = 3

∴ It is a geometric sequence

∴ The n^th term of a G.P is t_n = ar^n-1

∴ t₄ = 8 × 3^4-1

= 8 × 3³

= 8 × 27

= 216

t₅ = 8 × 3^5-1

= 8 × 3⁴

= 8 × 8

= 648

t₆ = 8 × 3^6-1

= 8 × 3⁵

= 8 × 243

= 1944

The next 3 terms are 8, 24, 72, 216, 648, 1944.