Question

Consider the recursive formula an = (2 + an-1) / 2

. The first term of the sequence is 10, what is the third term?
A) 1
B) 4
C) 6
D) 8

Answer 1

Answer: The correct option is B. The third term is 4.

Step-by-step explanation:

The given recursive formula is,

`a_n=(2+a_(n-1))/(2)`

It is given that the first term is 10. So,

`a_1=10`

To find third term, first we have to find the second term.

`a_2=(2+a_(2-1))/(2)`

`a_2=(2+a_(1))/(2)`

`a_2=(2+10)/(2)`

`a_2=(12)/(2)`

`a_2=6`

Therefore the second term is 6.

`a_3=(2+a_(3-1))/(2)`

`a_3=(2+a_(2))/(2)`

`a_3=(2+6)/(2)`

`a_3=(8)/(2)`

`a_3=4`

Therefore, the correct option is B. The third term is 4.