Fill in the blank space for the given series | vedclass

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(B) The given series is $2, 6, 18, 54, \ldots$Here,each term is obtained by multiplying the previous term by $3$.This is a Geometric Progression $(G.P

Vedclass · Accepted Answer

$4374$

Vedclass · Answer

(B) The given series is $2, 6, 18, 54, \ldots$Here,each term is obtained by multiplying the previous term by $3$.This is a Geometric Progression $(G.P.)$ where the first term $a = 2$ and the common ratio $r = 3$.The formula for the $n^{th}$ term of a $G.P.$ is $T_n = a \cdot r^{n-1}$.For the $8^{th}$ term $(n = 8)$:$T_8 = 2 \cdot 3^{8-1} = 2 \cdot 3^7$.Calculating $3^7 = 3 	imes 3 	imes 3 	imes 3 	imes 3 	imes 3 	imes 3 = 2187$.Therefore,$T_8 = 2 	imes 2187 = 4374$.

Fill in the blank space for the given series with the correct alternative.
In the series $2, 6, 18, 54, \ldots,$ what will be the $8^{th}$ term?

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Fill in the blank space for the given series with the correct alternative.In the series $2, 6, 18, 54, \ldots,$ what will be the $8^{th}$ term?