Question

Which term of the G.P. $2, 2\sqrt{2}, 4$,.....is 64 ?

• A. 9th term
• B. 7th term
• C. 4th term
• D. 11th term

Answer 1

Answer: (D)

11th term

Answer 2

From the given series First term, a = 2, Common ratio, $r = \frac{2 \sqrt{2}}{2} = \frac{4}{2 \sqrt{2}} = \sqrt{2}$ Now, nth term of G.P. = $ar^{n -1}$ $\therefore \, 64 = 2 (\sqrt{2} )^{n-1}$ $\Rightarrow \, (2)^{(n -1)/2} = 32 = 2^5$ $\Rightarrow \frac{n - 1}{2} = 5$ $\Rightarrow \, n = 11^{th}$ term