Question

The nth term of series 16,8,4.... is 1/2^17 the value of n is

Answer 1

nth term of series 16, 8, 4, ..... is 1/2^17

we can see that 16, 8, 4, ...... series is in GP
because common ratio of two consecutive terms is 1/2.

e.g.,first term , a = 16
common ratio, r = 1/2
use formula $t_n=ar^{n-1}$

so, 1/2^17 = 16(1/2)^{n-1}

=> 1/2^17 = 2^4/2^(n-1)

=> 1/2^17 = 1/2^(n - 1 - 4)

=> 1/2^17 = 1/2^(n-5)

=> 17 = n - 5

=> n = 17 + 5 = 22

hence, 22th term of given series is 1/2^17

Answer 2

HELLO DEAR,

GIVEN:-

nth term of series 16, 8, 4, ..... is 1/2^17

we can see that series are in gp

so,

first term , a = 16

common ratio, r = 1/2

we know formula for $\bold{a_n = ar^{n - 1}}$

so, $\bold{(1/2)^{17} = 16(1/2)^{n-1}}$

1/2^17 = 2^4/2^(n-1)

1/2^17 = 1/2^(n - 1 - 4)

1/2^17 = 1/2^(n-5)

on comparing both side,

we get,

17 = n - 5

n = 17 + 5

n = 22

HENCE, 22th term of given series is 1/2^17

I HOPE ITS HELP YOU DEAR,

THANKS