Question

Find the 8^th term of the sequence:

`3/4, 1 1/2, 3, ..............`

Answer 1

Given sequence: `3/4, 1 1/2, 3, ..............`

i.e. `3/4, 3/2, 3, .......`

Now,

`(3/2)/(3/4) = 2, 3/(3/2) = 2,`

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

Now, T_n = ar^{n – 1}

`\implies` T₈ = ar⁷

= `3/4xx2^((8 - 1))`

= `3/4 xx 2^7`

= `3/4 xx 2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 2`

= 96