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.