Question

Woo-Jin and Kiran were asked to find an explicit formula for the sequence 64\,,\,16\,,\,4\,,\,1,...64,16,4,1,...64, comma, 16, comma, 4, comma, 1, comma, point, point, point. Woo-Jin said the formula is f(n)

Answer 1

Neither Woo-Jin nor Kiran

Explanation:

Answer 2

`f(n)=64((1)/(4))^(n-1)`

Explanation:

The given sequence is

64, 16, 4, 1

`r_1=(a_2)/(a_1)=(16)/(64)=(1)/(4)`

`r_2=(a_3)/(a_2)=(4)/(16)=(1)/(4)`

`r_3=(a_4)/(a_3)=(1)/(4)`

It is a geometric series because it has a common ratio
`r_1=r_2=r_3=(1)/(4)`.

First term is 64.

The explicit formula of a geometric series is

`f(n)=ar^(n-1)`

where, a is first term and r is common ratio.

Substitute a=64 and r=1/4 in the above function.

`f(n)=64((1)/(4))^(n-1)`

Therefore, the required explicit formula is
`f(n)=64((1)/(4))^(n-1)`.