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

Question

asked Jul 12, 2018 133k views

2 Answers

Amin Saffar · Answer 1 · 2018-07-16T08:30:50+0000

Answer:

Option A is correct that is

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)