### Home > PC > Chapter 8 > Lesson 8.2.5 > Problem8-141

8-141.

Other recognizable functions can be found recursively. Consider the sequence defined by $a_{n+1} = a_{n} + 2n + 1$ where $a_{1} = 1$. Write the first five terms of the sequence. Then write a general (non-recursive) equation for the $n^{\text{th}}$ term.

$a_{n+1}= a_{n} + 2n + 1$
$a_{1} = 1$
$a_{2} = 1+ 2\left(1\right) + 1 = 4$
$a_{3} = 4 + 2\left(2\right) + 1 = 9$
$a_{4} = 9 + 2\left(3\right) + 1 = 16$
$a_{5} = 16 + 2\left(4\right) + 1 = 25$

$a_{n} = n^{2}$