CAT 2018 Quant Questions

Question:
The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ...+ 95 x 99 is

80707
80773
80730
80751
Show Answer
Correct Answer: 1

S = 7 x 11 + 11 x 15 + 15 x 19 + ...+ 95 x 99

Nth term of the series can be written as \({T_n} = (4n + 3)*(4n + 7)\)

Last term, (4n+3) = 95 i.e. n = 23

\(\sum\limits_{n = 0}^{n = 23} {(4n + 3)} *(4n + 7)\)

\( \Rightarrow \) \(\sum\limits_{n = 0}^{n = 23} 1 6{n^2} + 40n + 21\)

\( \Rightarrow \) \(16*\frac{{23*24*47}}{6} + 40*\frac{{23*24}}{2} + 21*23\)

\( \Rightarrow \) 80707

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CAT 2018 Quant Questions
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