Question

What are the first three terms of the sequence modeled by the recursive function an=1/2an-1 when a1=1?

A. 1, 1/2, 1/4
B. 1, 1/2, 0
C. 1, 2, 4
D. 1, 3/2, 2

Answer 1

A: 1,1/2,1/4

Explanation:

edg 2020

Answer 2

Option A is correct that is
`1,(1)/(2),(1)/(4)`

Explanation:

We have been given a formula
`a_n=(1)/(2)\cdot a_n-1`

`a_1=1`

We will put values of n in
`a_n=(1)/(2)\cdot a_n-1`

when n=2 we get

`a_2=(1)/(2)\cdot a_2-1`

`\Rightarrow a_2=(1)/(2)\cdot a_1`

`\Rightarrow a_2=(1)/(2)\cdot 1`

`\Rightarrow a_2=(1)/(2)`

when n=3

`a_3=(1)/(2)\cdot a_2`

`\Rightarrow a_3=(1)/(2)\cdot (1)/(2)`

`\Rightarrow a_3=(1)/(4)`

Therefore, Option A is correct that is
`1,(1)/(2),(1)/(4)`