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Q.

If the first term and common ratio of a G.P. are both $(\frac{1}{2}) (\sqrt{3} + i)$ , then the absolute value of its $n^{th}$ term is

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a

$4^{n}$

b

1

c

$3^{n}$

d

$2^{n}$

answer is C.

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Detailed Solution

In a Geometric progression

$a = r = \frac{\sqrt{3} + i}{2} \Rightarrow T_{n} = {ar}^{n - 1} = {(\frac{\sqrt{3} + i}{2})}^{n} ∴ |T_{n}| = {|\frac{\sqrt{3}}{2} + i (\frac{1}{2})|}^{n} = {(\sqrt{\frac{3}{4} + \frac{1}{4}})}^{n} = 1$

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If the first term and common ratio of a G.P. are both 123 + i , then the absolute value of its nth term is