Question

Which term of Gp 1/4,4,16...is equal to 16th term of Gp 2,4,8....​

Answer 1

10th term of first G.p. will be equal to 16th term of second G.P.

Step-by-step explanation:

For any geometric progression nth term is defined by the expression :

$T_{n}=ar^{n-1}$

where : a = first term of the sequence

             r = common ratio of the sequence

             n = number of term

For G.P. $\frac{1}{4},1,4,16....$

$T_{n}=ar^{n-1}$

    = $\frac{1}{4}(4)^{n-1}$

    = $4^{n-2}$

For G.P. 2, 4, 8........

$T_{n}=ar^{n-1}$

$T_{16}=2(2)^{16-1}$

Since $T_{n}$ of first G.P. = $T_{16}$ of second G.P.

$4^{n-2}$ = $2(2)^{16-1}$

$2^{2(n-2)}=2^{16}$

2(n-2) = 16

2n - 4 = 16

2n = 20

n = 10

Therefore, 10th term of first G.p. will be equal to 16th term of second G.P.

Learn more about geometric progression : https://brainly.in/question/11281733