Which term of the sequence 3 , 3,3 3 , ..... is 729? - Vidyadip

Question

Which term of the sequence $\sqrt { 3 } , 3,3 \sqrt { 3 }$ , ..... is 729?

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Answer

Here a = $\sqrt3$ , r = $\frac { 3 } { \sqrt { 3 } } = \sqrt { 3 }$ and a_n = 729
$\therefore$a_n = ar^n-1
$\Rightarrow 729 = \sqrt { 3 } \times ( \sqrt { 3 } ) ^ { n - 1 }$
$\Rightarrow ( \sqrt { 3 } ) ^ { 12 } = ( \sqrt { 3 } ) ^ { n }$
$\Rightarrow$n = 12
Therefore, 12^th term of the given G.P. is 729.

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