Answer
a) $36$ and $49$
b) $a_{n+1} = (\sqrt a_n + 1)^2$, $a_1 = 1$
c) $a_n = n^2$
Work Step by Step
a) Another way to write the sequence would be: $\{1^2, 2^2, 3^2, 4^2, 5^2,...\}$. Thus, the next two terms are $6^2$ and $7^2$ or $36$ and $49$.
b) The first term is $1$, so $a_1 = 1$
We have to find what value was squared in the previous term, add one, then square the new value to get the next term.
$a_{n+1} = (\sqrt a_n + 1)^2$
c) The term is simply the value of $n$ squared.
$a_n = n^2$
