The {n^{th}} term of the series 3 cdot 8 + 6 | vedclass

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Question

(A) The given series is $3 \cdot 8 + 6 \cdot 11 + 9 \cdot 14 + 12 \cdot 17 + \dots$The first factors of the terms are $3, 6, 9, 12, \dots$,which form

Vedclass · Accepted Answer

$3n(3n + 5)$

Vedclass · Answer

(A) The given series is $3 \cdot 8 + 6 \cdot 11 + 9 \cdot 14 + 12 \cdot 17 + \dots$The first factors of the terms are $3, 6, 9, 12, \dots$,which form an arithmetic progression with the first term $a = 3$ and common difference $d = 3$. The ${n^{th}}$ term is $a_n = 3 + (n - 1)3 = 3n$.The second factors of the terms are $8, 11, 14, 17, \dots$,which form an arithmetic progression with the first term $a = 8$ and common difference $d = 3$. The ${n^{th}}$ term is $b_n = 8 + (n - 1)3 = 3n + 5$.Therefore,the ${n^{th}}$ term of the given series is $T_n = a_n \cdot b_n = 3n(3n + 5)$.

The ${n^{th}}$ term of the series $3 \cdot 8 + 6 \cdot 11 + 9 \cdot 14 + 12 \cdot 17 + \dots$ will be

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