How many terms of the geometric series `1+4+16+64+`will make the sum ` – InterviewSolution

InterviewSolution

1.	How many terms of the geometric series `1+4+16+64+`will make the sum `5461`?
Answer» Let the required number of terms be n. Here, `a=1, r=4 gt 1` and `S_(n)=5461`. `:. S_(n)=(a(r^(n)-1))/((r-1)) rArr (1xx(4^(n)-1))/((4-1))=5461` `rArr (4^(n)-1)=16383` `rArr 4^(n)=16384=4^(7)` `rArr n=7`. Hence, the required number of terms is 7.

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