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

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(B) The given series is $2 \times 4 + 4 \times 6 + 6 \times 8 + \dots$The ${n^{th}}$ term of the series can be written as ${T_n} = (2n) \times (2n + 2) = 4n(n + 1)$.To find the ${20^{th}}$ term,we substitute $n = 20$ into the formula:${T_{20}} = 4 \times 20 \times (20 + 1)$${T_{20}} = 80 \times 21$${T_{20}} = 1680$.Thus,the correct option is $B$.

Competitive Quantitative Aptitude Progression and Sequence Progression and Sequence

Easy

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

A
$1600$
B
$1680$
C
$420$
D
$840$

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Progression and Sequence

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Progression and Sequence

If the first term of an $A.P.$ is $10$,the last term is $50$,and the sum of all the terms is $300$,then the number of terms is:

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The value of $\overline{0.037}$,where $\overline{0.037}$ stands for the number $0.037037037...$,is:

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If all roots of the equation $x^3 - 2ax^2 + 3bx - 8 = 0$ are positive,where $a, b \in R$,then the minimum value of $b$ is:

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If the sum of the series $2 + 5 + 8 + 11 + \dots$ is $60100$, then the number of terms is:

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For any odd integer $n \ge 1$,${n^3} - {(n - 1)^3} + ........... + {( - 1)^{n - 1}}{1^3} = $

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

Similar Questions

If the first term of an $A.P.$ is $10$,the last term is $50$,and the sum of all the terms is $300$,then the number of terms is:

The value of $\overline{0.037}$,where $\overline{0.037}$ stands for the number $0.037037037...$,is:

If all roots of the equation $x^3 - 2ax^2 + 3bx - 8 = 0$ are positive,where $a, b \in R$,then the minimum value of $b$ is:

If the sum of the series $2 + 5 + 8 + 11 + \dots$ is $60100$, then the number of terms is:

For any odd integer $n \ge 1$,${n^3} - {(n - 1)^3} + ........... + {( - 1)^{n - 1}}{1^3} = $

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