Third term of a G.P. is square of first term. If second term is 8 , then {6^{th}} term is

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8. Sequences and Series

easy

The third term of a $G.P.$ is the square of first term. If the second term is $8$, then the ${6^{th}}$ term is

A

$120$

B

$124$

C

$128$

D

$132$

Solution

(c) ${a^2} = a{r^2}$

$ \Rightarrow $ $a = {r^2}$. Also $ar = 8$

$ \Rightarrow $ $r = 2$ and $a = 4$.

$\therefore $ ${T_6} = a{r^5} = 4 \times {2^5} = 128$.

Standard 11

Mathematics

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