The 20^{th} term of the series 2 times 4 + 4 | vedclass

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(B) The given series is $2 	imes 4 + 4 	imes 6 + 6 	imes 8 + \dots$The $n^{th}$ term $T_n$ can be written as the product of the $n^{th}$ term of th

Vedclass · Accepted Answer

$1680$

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(B) The given series is $2 	imes 4 + 4 	imes 6 + 6 	imes 8 + \dots$The $n^{th}$ term $T_n$ can be written as the product of the $n^{th}$ term of the sequence $2, 4, 6, \dots$ and the $n^{th}$ term of the sequence $4, 6, 8, \dots$The $n^{th}$ term of $2, 4, 6, \dots$ is $2n$.The $n^{th}$ term of $4, 6, 8, \dots$ is $2(n + 1)$.Thus,$T_n = 2n 	imes 2(n + 1) = 4n(n + 1)$.For the $20^{th}$ term,substitute $n = 20$:$T_{20} = 4 	imes 20 	imes (20 + 1) = 80 	imes 21 = 1680$.

The $20^{th}$ term of the series $2 \times 4 + 4 \times 6 + 6 \times 8 + \dots$ will be

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