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

Slot -2 – Quantitative Aptitude – Modern Maths – Sequence and Series – The value of the sum 7 x 11

The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + …+ 95 x 99 is?

a) 80707
b) 80730
c) 80773
d) 80751

Answer: a) 80707

Solution: 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
Correct option a) 80707

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