Question

which term of the series 9,6,4,........is 64/81

Answer 1

Answer:

which term of the series 9,6,4,8,1 is 64/81

Answer 2

The correct answer is 7.

Given: Sequence = 9, 6, 4......

To Find: Which term is  $\frac{64}{81}$.

Solution:

In the sequence 9, 6, 4......

r = $\frac{second term}{first term}$

r = $\frac{6}{9} =\frac{2}{3}$.

nth term in GP = $ar^{n-1}$

a is first term.

r is common ratio.

$9*\frac{2}{3} ^{n-1}=\frac{64}{81}$

$\frac{2}{3} ^{n-1}=\frac{64}{81}*\frac{1}{9}$

$\frac{2}{3} ^{n-1}=\frac{2^{6} }{3^{4} }*\frac{1}{3^{2} }$

$\frac{2}{3} ^{n-1}=\frac{2^{6} }{3^{6} }$

As the bases are equal, so we can compare powers.

n-1 = 6

n = 7

Hence, the term $\frac{64}{81}$ is 7th term.

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