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Question
Which term of the following sequence:
`sqrt3, 3, 3sqrt3`, .... is 729?
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Solution
The given sequence is `sqrt3, 3, 3sqrt3`,...
Here, a = `sqrt3` and r = `3/sqrt3 = 3`
Let the nth term of the given sequence be 729.
an = arn- 1
∴ arn - 1 = 729
= `(sqrt3)(sqrt3)^("n" - 1)` = 729
= `(3)^(1/2) (3)^((n - 1)/2) = (3)^6`
= `(3)^(1/2 + (n - 1)/2) = (3)^6`
∴ `1/2 + (n - 1)/2 = 6`
= `(1 + n - 1)/2 = 6`
= n = 12
Thus, the 12th term of the given sequence is 729.
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