The n^{th} term of the series 3.8 + 6.11 + 9. | vedclass

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Question

(A) The given series is $3.8 + 6.11 + 9.14 + 12.17 + .....$The series consists of products of two terms.The first factors are $3, 6, 9, 12, .....$,whi

Vedclass · Accepted Answer

$3n(3n + 5)$

Vedclass · Answer

(A) The given series is $3.8 + 6.11 + 9.14 + 12.17 + .....$The series consists of products of two terms.The first factors are $3, 6, 9, 12, .....$,which form an Arithmetic Progression $(AP)$ with the first term $a = 3$ and common difference $d = 3$.The $n^{th}$ term of this sequence is $a_n = a + (n - 1)d = 3 + (n - 1)3 = 3n$.The second factors are $8, 11, 14, 17, .....$,which form an $AP$ with the first term $a = 8$ and common difference $d = 3$.The $n^{th}$ term of this sequence is $b_n = 8 + (n - 1)3 = 8 + 3n - 3 = 3n + 5$.Therefore,the $n^{th}$ term of the given series is the product of the $n^{th}$ terms of the two sequences:$T_n = (3n) 	imes (3n + 5) = 3n(3n + 5)$.

The $n^{th}$ term of the series $3.8 + 6.11 + 9.14 + 12.17 + .....$ will be

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