InterviewSolution
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InterviewSolution
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In a finite G.P. the product of the terms equidistant from thebeginning and the end is always same and equal to the product of first andlast term. |
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Answer» Let `a, ar,ar^2,ar^3...ar^(n-1)`is the G.P. with first term as `a` and common ratio `r`. Then, `k` th term from the beginning ` = ar^(k-1)` Now, `k` th term from the end will be `n-k+1` th term from the beginning. So, `n-k+1` th term from the beginning `= ar^(n-k+1-1) = ar^(n-k)` Now, product of `k` th term from the beginning and end `= ar^(k-1)*ar^(n-k)` `= a*ar^(k-1+n-k)` `=a*ar^(n-1)` `=` Product of first and last term of the G.P. Hence, in a finite G.P. the product of the terms equidistant from the beginning and the end is always same and equal to the product of first and last term. |
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