Question

8A) which term of G.P 1/4,4,16--- is equal to 16th
termoff.P.2.4.8--- ?​

Answer 1

Answer:

10th term

Step-by-step explanation:

1st series of GP = 1/4, 1, 4, 16 ......

nth term = ar^(n-1)

a = 1/4 r = 4

$nth \: term \: = \frac{1}{4} \times {4}^{n - 1} \\ = {4}^{ - 1} \times {4}^{n - 1} \\ = {4}^{ - 1 + n - 1} = {4}^{n - 2} \\ = { {(2}^{2} )}^{n - 2} \\ = {2}^{2n - 4}$

2nd series of GP = 2, 4, 8.......

a = 2 r = 2

$16th \: term = 2 \times {2}^{15} \\ = {2}^{16}$

we need the number of terms of 1st series which is equal to 16th term 2^16 of 2nd series

${2}^{2n - 4} = {2}^{16} \\ bases \: are \: same \: power \: will \: be \: equated \\ 2n - 4 = 16 \\ 2n = 16 + 4 \\ 2n = 20 \\ n = \frac{20}{2} \\ n = 10$

therefore the tenth term of 1 GP is equal to the 16th term of 2nd GP

hope you get your answer