### Home > PCT > Chapter Ch8 > Lesson 8.2.5 > Problem 8-141

8-141.

Other recognizable functions can be found recursively. Consider the sequence defined by *a _{n}*

_{+1}=

*a*+ 2

_{n}*n*+ 1 where

*a*

_{1}= 1. Write the first five terms of the sequence. Then write a general (non-recursive) equation for the nth term.. Homework Help ✎

*a _{n}*

_{+1}=

*a*+ 2

_{n}*n*+ 1

*a*

_{1}= 1

*a*

_{2}= 1+ 2(1) + 1 = 4

*a*

_{3}= 4 + 2(2) + 1 = 9

*a*

_{4}= 9 + 2(3) + 1 = 16

*a*

_{5}= 16 + 2(4) + 1 = 25

*a _{n}* =

*n*

^{2}