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Ex 9.4, 6 - Find sum 3 x 8 + 6 x 11 + 9 x 14 - Chapter 9 Class 11 - Finding sum from nth number

  1. Chapter 9 Class 11 Sequences and Series
  2. Serial order wise
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Ex 9.4, 6 Find the sum to n terms of the series 3 × 8 + 6 × 11 + 9 × 14 +… Step 1: Finding nth term an an = (nth term of 3, 6, 9 …) × (nth term of 8, 11, 14, …) an = (3n)(3n + 5) = 9n2 + 15n Step 2: Finding sum of n terms = 9 × (n(n+1)(2n+1))/6 +15 × (n(n+1))/2 = 9𝑛(𝑛 + 1)(2𝑛 + 1)/6 + (15𝑛(𝑛 + 1))/2 = (3n(n+1)(2n+1))/2 + (15n(n+1))/2 = (3n(n+1))/2 [(2n+1)+5] = (3n(n+1))/2 [2n+1+5] = (3n(n+1))/2 [2n+6] = 3/2n(n+1) 2(n+3) = 3n(n + 1)(n + 3) Hence, The required sum is 3n(n + 1)(n + 3)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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