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in Geometric Progressions by (15.2k points)

Which term of the GP \(\frac{1}{4}, \frac{-1}{2} , 1 ..... \) is -128?

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Given GP is \(\frac{1}{4}, \frac{-1}{2}, 1 ......\) is -128?

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

Where r is the common ratio.

The first term in the given GP, a = a1 = 1/4

The second term in GP, a2 = -1/2

Now, the common ratio, r = a2/a1

\(r = -\frac{4}{2} = -2 \)

Let us consider -128 as the nth term of the GP.

Now, nth term of GP is, an = arn – 1

So, -128 is the 10th term in GP.

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