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Question

In the geometric series 2+4+8+...., starting from the first term how many consecutive terms are needed to yield the sum 1022?

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Solution

Given the geometric series is 2+4+8+...
Let n be the number of terms required to get the sum.
Here a=2,r=2,Sn=1022.
To find n, let us consider
Sn=a[rn1]r1 if r1
=(2)[2n11]=2(2n1).
But Sn=1022 and hence 2(2n1)=1022
2n1=511
2n=512=29
Thus, n=9

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