Question

which term of G. P.1/4,4, 16 is equal to 16th term od G. P. 2,4,8...​

Answer 1

the 10th term of GP $\dfrac{1}{4} ,\ 4 , \ 16 , ........$ is equal to the 16th term of GP $2 , 4 , 8, ........$ .

Explanation:

Formula :

nth term of GP = $a_n=ar^{n-1}$ , where a= first term and r = common ratio.

First GP = $\dfrac{1}{4} ,\ 4 , \ 16 , ........$

Second GP = $2 , 4 , 8, ........$

In second GP ,

a= 2  , r = $\dfrac{4}{2}=2$

16th term = $(2)(2)^{16-1}= (2)2^{15}=2^{16}=65536$

In first GP , a= $\dfrac{1}{4}$  and $r=\dfrac{16}{4}=4$

Now , as per question ,

$\dfrac{1}{4}(4)^{n-1}=2^{16}= 2^{2\times8}= (2^2)^8=4^8\\\\ (4)^{n-1} = 4\times4^8=4^{9}\\\\ (4)^{n-1} = 4^9\\\\ n-1=9\\\\ n=10$

Hence, the 10th term of GP $\dfrac{1}{4} ,\ 4 , \ 16 , ........$ is equal to the 16th term of GP $2 , 4 , 8, ........$ .

# Learn more :

The 3rd and the 8th term of a G. P. are 4 and 128 respectively. Find the G. P.

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