Question

.Find the G.P in which the 2nd term is √6 and the 6th term is 9√6
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Answer 1

$\small\green{☘︎}\red{Answer \: to \: the \: Question \: } {✔︎}$

We know that the formula for the nth term of an G.P is Tn=arn−1, where a is the first term, r is the common ratio.

It is given that the 2nd term is T2=6, therefore,

 

T2=ar2−1⇒6=ar⇒a=r6..(1)  

It is also given that the 6th term is T6=96, therefore using equation 1,

 

T6=ar6−1⇒96=r6×r5⇒696=r4⇒r4=9⇒(r2)2=32⇒r2=3⇒r=3 

Now, substitute the value of r in equation 1:

a=36=36=2 

Therefore, the terms of G.P are:

a1=2a2=a1×r=2×3=6a3=a2×r=6×3=18=32a4=a3×r=18×3=54=36    

Hence, the G.P is 2,6,32,36,.