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Question

What is the average of the first 300 terms of the given sequence?
1,−2,3,−4,5,−6,.....,n.(−1)n+1

A
1
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B
0.5
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C
0
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D
0.5
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Solution

The correct option is D 0.5
Avg =[1+3+5+7+...+(2n1)][2+4+6+...+2n]n
Here n=300
No. of even terms =150
No. of odd terms =150
Now,
1+3+5+7+...+150termsSn=n2[2a+(n1)d]Sn1=1502[2×1+149×2]=22500
and 2+4+6+8+....+150termsSn=n2[2a+(n1)d]Sn2=1502[2×2+149×2]=22650
Average =Sn1Sn2300=2250022650300=0.5

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