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Question

12+34+78+1516+....100 terms =


A

2100+99

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B

2-100+99

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C

2-101+99

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D

2-99+99

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Solution

The correct option is B

2-100+99


Explanation for the correct option:

Step1. Find the sum 12+34+78+

=112+114+118+

=1+1+1+12+14+18

=n-12+14+18... 1+1+1+....=n

The second series is a GP

Here, a=12,r=12

Step 2. Apply the formula a(1rn)1r in second series, we get

=n12112n12

=n1-2n

=2-n+n-1

Put n=100

=2-100+100-1

=2-100+99

Hence, Option ‘B’ is Correct.


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