### Home > PC > Chapter 8 > Lesson 8.2.5 > Problem 8-142

8-142.

Given the sequence defined by

*a*_{n}_{+1 }=where *a*_{1}= 1. What is the limit of the sequence? Homework Help ✎ Using the process as described in problem 8-135, estimate the limit.

We can find the limit using algebra by solving the equation L =

. Solve the equation to find the exact value of the limit.

*a*_{5} =*a*_{6} =*a*_{7} =*a*_{8} =*a*_{9} =*a*_{10} =

*L*^{2} = 1 + *L**L*^{2} − *L* − 1 = 0

Use the quadratic formula!