6. Find the number of terms in the geometric progression 6, 12, 24, ..., 1536.

Question

<!--[if !supportLists]-->1.    <!--[endif]-->Find the number of terms in the geometric progression 6, 12, 24, ..., 1536.

Answer 1

common ratio, r = 12/6 =2

nth term of geometric progression is given by, a_n = a₁ * r^n-1

In this question , a_n = 1536, a₁ = 6 and r =2

therefore, 1536 = 6 * 2^n-1

or 2^n-1= 1536/6

or 2^n-1= 256

or 2^n-1= 2⁸

or n-1 = 8

or n =9

So there are 9 terms in the given progression.