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Class 11
Mathematics
Sequence and Series
find the sum to nbsp n nbsp terms of the series 3...

Question:
Find the sum to n terms of the series 3 × 8 + 6 × 11 + 9 × 14 +…

Answer:

The given series is 3 × 8 + 6 × 11 + 9 × 14 + …

an = (nth term of 3, 6, 9 …) × (nth term of 8, 11, 14, …)

= (3n) (3n + 5)

= 9n² + 15n

$therefore space S subscript n space equals space sum from k equals 1 to n of space a subscript k space equals space sum from k equals 1 to n of space open parentheses 9 k squared space plus space 15 k close parentheses space space space space space space space space space space space equals space 9 sum from k equals 1 to n of space k squared space plus space 15 space sum from k equals 1 to n of space k space space space space space space space space space space space equals space 9 space cross times space fraction numerator n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses over denominator 6 end fraction plus 15 cross times fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction space space space space space space space space space space space space equals fraction numerator 3 n open parentheses n plus 1 close parentheses over denominator 2 end fraction open parentheses 2 n plus 1 plus 5 close parentheses space space space space space space space space space space space space equals fraction numerator 3 n open parentheses n plus 1 close parentheses over denominator 2 end fraction open parentheses 2 n plus 6 close parentheses space space space space space space space space space space space space space space equals space 3 n open parentheses n plus 1 close parentheses open parentheses n plus 3 close parentheses$

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Question:
Find the sum to n terms of the series 3 × 8 + 6 × 11 + 9 × 14 +…

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Question: Find the sum to n terms of the series 3 × 8 + 6 × 11 + 9 × 14 +…

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Question:
Find the sum to n terms of the series 3 × 8 + 6 × 11 + 9 × 14 +…