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in Geometric Progressions by (15.2k points)

Which term of the GP 3, 6, 12, 24…. Is 3072?

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1 Answer

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by (15.7k points)

Given GP is 3, 6, 12, 24…. 

The given GP is of the form, a, ar, ar2 , ar3…. 

Where r is the common ratio. 

First term in the given GP, a1 = a = 3 

Second term in GP, a2 = 6

Now, the common ratio, \(r = \frac{a_2}{a_1}\)

r = \(\frac{6}{3} = 2\)

Let us consider 3072 as the nth term of the GP. 

Now, nth term of GP is, an = arn – 1

3072 = 3.2n-1

\(\frac{3072 \times 2}{3} = 2^n\)

2n = 211n = 11 

So, 3072 is the 11th term in GP.

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