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The value of the sum 7 x 11 | Quantitative Aptitude - Modern Maths - Sequence and Series

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The question below is from previous year CAT question from CAT 2018 exam comes from CAT Modern Maths – Sequence and Series – The value of the sum 7 x 11 … . Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

CAT 2018 – Slot 2 - Sequence and Series - Question 1 - The value of the sum 7 x 11

Q. 1:The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + …+ 95 x 99 is
1. 80707
2. 80773
3. 80730
4. 80751

7 x 11 + 11 x 15 + 15 x 19 + …+ 95 x 99

nth term of series = {4(n+1)-1}×{ 4 (n+1)+3}=16n^2+16+32n+8n+8-

3=16n^2+40n+21

Thus 7 x 11 + 11 x 15 + 15 x 19 + …+ 95 x 99 = ∑ Tn=∑ (16n^2+40n+15)

Required sum = ∑ Tn=∑ (16n^2+ 40n+15)=16 ×(n(n+1(2n+1))/6 + 40×n(n+1)/2 + 21n

Putting n= 23

Sum = 16×23×24×47/6+40×23×24/2+21×23

=69184+11040+483=80707

 

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