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Question

The sum of 40 terms of the series 1+2+3+4+5+8+7+16+9+...... is,

A
398+220
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B
398+221
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C
398+219
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D
None of these
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Solution

The correct option is C 398+221
The given series X=1+2+3+4+5+8+7+16+9+....
This is sum of 2 series X1 and X2
X1+X2=X
X1=1+3+5+7+9+.......
X2=2+4+8+16+.......
X1 is an AP with first term 1 and common difference 2
X2 is a GP with first term 2 and common ratio 2
Now for sum up to 40 term for X, we need to find sum of first 20 terms of the GP and first 20 terms of AP.
Sum of AP =SAP =202(2+(201)2)=10(2+38)=400

Sum of GP =SGP=2(1220)12=2+221

So, Sum X =4002+221 = 398+221


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