Fill in the blank space for the given series | vedclass

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Question

(A) The given series is $3, 12, 27, 48, 75, 108, \dots$We can observe that each term follows the pattern $3 	imes n^{2}$,where $n$ is the position of

Vedclass · Accepted Answer

$147$

Vedclass · Answer

(A) The given series is $3, 12, 27, 48, 75, 108, \dots$We can observe that each term follows the pattern $3 	imes n^{2}$,where $n$ is the position of the term:$3 	imes 1^{2} = 3 	imes 1 = 3$$3 	imes 2^{2} = 3 	imes 4 = 12$$3 	imes 3^{2} = 3 	imes 9 = 27$$3 	imes 4^{2} = 3 	imes 16 = 48$$3 	imes 5^{2} = 3 	imes 25 = 75$$3 	imes 6^{2} = 3 	imes 36 = 108$The next term in the series corresponds to $n = 7$:Missing number $= 3 	imes 7^{2} = 3 	imes 49 = 147$.

Fill in the blank space for the given series with the correct alternative.
$3, 12, 27, 48, 75, 108, (...)$

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Fill in the blank space for the given series with the correct alternative.$3, 12, 27, 48, 75, 108, (...)$