Question

Consider the recursive formula an = 2 + an-1 2 . The first term of the sequence is 10, what is the third term?

Answer 1

Answer:

the answer is 4

Answer 2

Answer:

Hence, the third term of the sequence is:

4

Step-by-step explanation:

We are given a recursive formula as:

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

We are given first term of the sequence as:

$a_1=10$

Now, we are asked to find the third term of the sequence.

i.e. $a_3$

Now, using recursive formula we have:

$a_2=\dfrac{2+a_1}{2}\\\\a_2=\dfrac{2+10}{2}\\\\a_2=\dfrac{12}{2}\\\\a_2=6$

Similarly,

$a_3=\dfrac{2+a_2}{2}]\\\\a_3=\dfrac{2+6}{2}\\\\a_3=\dfrac{8}{2}\\\\a_3=4$

Hence, the third term of the sequence is:

4