Class 11 Mathematics - Chapter Sequence and Series NCERT Solutions | Find the sum to n terms of the

Welcome to the NCERT Solutions for Class 11th Mathematics - Chapter Sequence and Series. This page offers a step-by-step solution to the specific question from Excercise ".$ex_no." , Question 6: find the sum to nbsp n nbsp terms of the series 3....
Question 6

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 + …

a= (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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