Question

which term of GP is 1,2,4,8.......is256?

Answer 1

Answer:

GP = 1, 2, 4, 8 .... 256.

To find : 256 is which term

=> a = 1, r = 2

The nth term of a GP is given by: arⁿ⁻¹

=> arⁿ⁻¹ = 256

=> 1 . ( 2 )ⁿ⁻¹ = 256

=> 2ⁿ⁻¹ = 256

256 can be written as 2⁸

=> 2ⁿ⁻¹ = 2⁸

Bases are same so equate the powers. Hence we get,

=> n - 1 = 8

=> n = 9

Hence 256 is the 9th term of the given GP.

Answer 2

Given,

        a = 1 , r = second term / first term

                    = 2/1 = 2

We have the find the value of n ?

tn = 256

Formula :- $tn= ar^{n-1}$

         '' Substituting all the given values in the given formula''

256 = 1 × 2ⁿ⁻¹

= 2⁸ = 2⁽ⁿ⁻¹⁾ ; n - 1 = 8

         n = 9        

Therefore, the 9th term is 256.