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Question:
The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ...+ 95 x 99 is
The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ...+ 95 x 99 is
Updated On: Sep 30, 2024
- 80707
- 80773
- 80730
- 80751
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The Correct Option is A
Solution and Explanation
The correct answer is (A):
N th term of the series can be written as
tn (4n 3)(4n 7)
= 16n2 + 40n + 21
∑tn = 16∑n2 + 40∑n + 21∑1
= 16n(n+1)(2n+1) / 6+40n(n+1) / 2+21
here n = 23 (7, 11, 15….. 95 is an AP with common different 4 with 23 terms)
∑tn = 16×23×24×47 / 6+20×23×24+21×23
= 80707
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