The third term of a G.P. is the square of the | vedclass

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(C) Let the first term be $a$ and the common ratio be $r$.The terms of the $G.P.$ are $a, ar, ar^2, ar^3, \dots$The third term is $ar^2$ and the first

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$128$

Vedclass · Answer

(C) Let the first term be $a$ and the common ratio be $r$.The terms of the $G.P.$ are $a, ar, ar^2, ar^3, \dots$The third term is $ar^2$ and the first term is $a$.Given that the third term is the square of the first term: $ar^2 = a^2$.Since $a 
eq 0$,we have $a = r^2$.The second term is $ar = 8$.Substituting $a = r^2$ into the second term equation: $(r^2)r = 8 \Rightarrow r^3 = 8 \Rightarrow r = 2$.Then $a = r^2 = 2^2 = 4$.The $6^{th}$ term is $T_6 = ar^5$.$T_6 = 4 	imes 2^5 = 4 	imes 32 = 128$.

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

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