The 3^{rd} term of a G.P. is the square of th | vedclass

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(C) Let $a$ be the first term and $r$ be the common ratio of the $G.P.$The $n^{th}$ term of a $G.P.$ is given by $a_n = ar^{n-1}$.Given that the $3^{r

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$128$

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(C) Let $a$ be the first term and $r$ be the common ratio of the $G.P.$The $n^{th}$ term of a $G.P.$ is given by $a_n = ar^{n-1}$.Given that the $3^{rd}$ term is the square of the first term:$a_3 = (a_1)^2$$ar^2 = a^2$Since $a 
eq 0$,we divide by $a$ to get $r^2 = a$ $....(1)$Given that the $2^{nd}$ term is $8$:$a_2 = ar = 8$ $....(2)$Substitute $a = r^2$ from equation $(1)$ into equation $(2)$:$(r^2)r = 8$$r^3 = 8$$r = 2$Now,find $a$ using $a = r^2$:$a = (2)^2 = 4$We need to find the $6^{th}$ term $(a_6)$:$a_6 = ar^5$$a_6 = 4 	imes (2)^5$$a_6 = 4 	imes 32 = 128$Therefore,the $6^{th}$ term is $128$.

The $3^{rd}$ term of a $G.P.$ is the square of the first term. If the second term is $8,$ determine the $6^{th}$ term.

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