S -1002-992-982-972-22-12 - what is the value of S -A- 5050B- 5024C- 5000D- 2020

The correct option is A 5050 (100^2 99^2) + (98^2 97^2) + .................. + (2^2 1^2) = 199 + 195 + 191 + 187 + ......................... + 3 =(199+3) ...

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Quantitative Aptitude

Sum of Consecutive Numbers

S =1002-992+9...

Question

$S = 100^{2} - 99^{2} + 98^{2} - 97^{2} + . . . . . . . . . . . . . . . . . . . . . . . . + 2^{2} - 1^{2};$ what is the value of S?

2020

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5050

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5024

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5000

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Solution

The correct option is B
5050

$(100^{2} - 99^{2}) + (98^{2} - 97^{2}) + . . . . . . . . . . . . . . . . . . + (2^{2} - 1^{2})$

= 199 + 195 + 191 + 187 + ......................... + 3
$= (199 + 3) \times \frac{50}{2} = 5050.$
Even simpler way of calculation would be:
(100+99)+(98+97)+...+(2+1)
= Sum of first 100 natural numbers $= \frac{100 \times 101}{2} = 5050$

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Similar questions

Q. The value of

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is:

100^{2} - 99^{2} + 98^{2} - 97^{2} + 96^{2} + 95^{2} + . . . . = S

find

S = ?

Q. The least value of

(x + 100)^{2} + (x + 99)^{2} + \dots \dots + (x + 1)^{2} + x^{2} + (x - 1)^{2} + (x - 2)^{2} + \dots . + (x - 100)^{2}

Q. The least value of

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S=1002−992+982−972+........................+22−12; what is the value of S?

The correct option is B 5050 (1002−992)+(982−972)+..................+(22−12) = 199 + 195 + 191 + 187 + ......................... + 3 =(199+3)×502=5050. Even simpler way of calculation would be: (100+99)+(98+97)+...+(2+1) = Sum of first 100 natural numbers =100×1012=5050

$S = 100^{2} - 99^{2} + 98^{2} - 97^{2} + . . . . . . . . . . . . . . . . . . . . . . . . + 2^{2} - 1^{2};$ what is the value of S?