Question

Find the sixth term of the series :

2², 2³, 2⁴, ...................

Answer 1

Given sequence: 2², 2³, 2⁴, ...................

Now,

`2^3/2^2 = 2, 2^4/2^3 = 2`

Since `2^3/2^2 = 2^4/2^3 = ....... = 2,` the given sequence is a G.P. with first term, a = 2² = 4 and common ratio, r = 2.

Now, T_n = ar^{n – 1}

∴ T₆ = 4 × (2)⁵

= 4 × 32

= 128