SarkariPYQ

SSC CGL 2022 PYQ — Question 62

SSC CGL - 05 Dec 2022 - Shift 3 • Quantitative Aptitude • Q62

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What is the value of

1002−992+982−972+962−952+942−932....122−112?100^2-99^2+98^2-97^2+96^2-95^2+94^2-93^2....12^2-11^2?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 4995

Formula used:

Sum = n/2(a + l)           ---- (1)

Where n =  number of terms, a = first term and l = last term

Calculations:

⇒ 1002−992+982−972+962−952+942−932....122−112100^2-99^2+98^2-97^2+96^2-95^2+94^2-93^2....12^2-11^2

Can be written as;

⇒ (100 + 99)(100 - 99) + (98 + 97)(98 - 97) + ......... (12 + 11)(12 - 11)

⇒ 100 + 99 + 98 + 97 + ..................... + 12 + 11

Where, n = 90

l = 11 and a = 100

Using equation (1), we get

Sum = 90/2(100 + 11)

⇒ 4995