SELECT * FROM question_mgmt as q WHERE id=1052 AND status=1 SELECT id,question_no,question,chapter FROM question_mgmt as q WHERE courseId=2 AND subId=6 AND chapterId=80 and ex_no='4' AND status=1 ORDER BY CAST(question_no AS UNSIGNED)

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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