Question

Which term of the GP 27,-18,12,-8 .... Is 1024/2187

Answer 1

11th term of the given GP is 1024/2187.

Step-by-step explanation:

The given GP is

27,-18,12,-8 ....

First term = 27

Common ratio = $\frac{-18}{27}=-\frac{2}{3}$

The nth term of a GP is

$a_n=ar^{n-1}$

where, a is first term and r is common ratio.

Substitute a=27 and r=-2/3 in the above formula.

$a_n=(27)(-\frac{2}{3})^{n-1}$

It is given that nth term of GP is 1024/2187.

$\frac{1024}{2187}=(27)(-\frac{2}{3})^{n-1}$

Divide both sides by 27.

$\frac{1024}{59049​}=(-\frac{2}{3})^{n-1}$

$(-\frac{2}{3})^{10}=(-\frac{2}{3})^{n-1}$

On comparing both sides we get

$n-1=10$

$n=11$

Therefore, the 11th term of the given GP is 1024/2187.

#Learn more:

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