Question

which term of G.P 1,√3,3 ....... will be 81

Answer 1

Nth term=ar^(n-1)
81=1(√3)^(n-1)
n=9

Answer 2

81 is the 9th term in the G.P.

Step-by-step explanation:

Given:

G.P. is 1,√3,3.........81.

The common ratio "r" is given by

$\rightarrow \: r = \frac{ \sqrt{3} }{1} = \sqrt{3}$

The first term "a" is 1.

The nth term of an G.P. is given by

$\rightarrow \: a {r}^{n - 1}$

As given nth term of an G.P. is 81.

$\rightarrow \: 81 = 1 \times { (\sqrt{3} )}^{n - 1} \\ \rightarrow \: 81 = { ({3}^{ \frac{1}{2} }) }^{n - 1} \\ \rightarrow \: {3}^{4} = {(3)}^{ \frac{n - 1}{2} } \\ \rightarrow \: 4 = \frac{n - 1}{2} \\ \rightarrow \: n - 1 = 8 \\ \rightarrow \: n = 9$

So, 81 is the 9th term in the G.P.