Question

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

Answer 1

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

Explanation:

The given recursive formula is,

$a_n=\frac{2+a_{n-1}}{2}$

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.

$a_2=\frac{2+a_{2-1}}{2}$

$a_2=\frac{2+a_{1}}{2}$

$a_2=\frac{2+10}{2}$

$a_2=\frac{12}{2}$

$a_2=6$

Therefore the second term is 6.

$a_3=\frac{2+a_{3-1}}{2}$

$a_3=\frac{2+a_{2}}{2}$

$a_3=\frac{2+6}{2}$

$a_3=\frac{8}{2}$

$a_3=4$

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