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Question 6 - Finding sum from nth number - Chapter 8 Class 11 Sequences and Series
Last updated at April 16, 2024 by Teachoo
Chapter 8 Class 11 Sequences and Series
Concept wise
- Finding Sequences
- Arithmetic Progression (AP): Formulae based
- Arithmetic Progression (AP): Statement
- Arithmetic Progression (AP): Calculation based/Proofs
- Inserting AP between two numbers
- Arithmetic Mean (AM)
- Geometric Progression(GP): Formulae based
- Geometric Progression(GP): Statement
- Geometric Progression(GP): Calculation based/Proofs
- Inserting GP between two numbers
- Geometric Mean (GM)
- AM and GM (Arithmetic Mean And Geometric mean)
- AP and GP mix questions
- Finding sum from series
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Finding sum from nth number
Transcript
Question 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 = 9 ( + 1)(2 + 1)/6 + (15 ( + 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)
