Question

Find the G.P. in which the 2nd term is √6 and 6th term is 9√6

Answer 1

Step-by-step explanation:

2nd term of GP = a × r=✓6

6th term of GP = a × r^5 = 9√6

divide 6th term by 2nd term

$\frac{a \times {r}^{5} }{a \times r} = \frac{9 \sqrt{6} }{ \sqrt{6} } \\ {r}^{4} = 9 \\ r = \sqrt[4]{9} = \sqrt{3} \\ a \times r = \sqrt{6} \\ a \times \sqrt{3} = \sqrt{6} \\ a = \frac{ \sqrt{6} }{ \sqrt{3} } = \sqrt{2} \\ the \: gp \: is \\ a \: \: \: \: ar \: \: \: \: a {r}^{2} \: \: \: \: \: a {r}^{3} \\ \sqrt{2} \: \: \: \: \: \: \sqrt{6} \: \: \: \: 3 \sqrt{2} \: \: \: \: 3 \sqrt{6} \: \: \: \: 9 \sqrt{2} \: \: \: \: \: \: 9 \sqrt{6} ........$