Assume that the sequence converges and find its limit.
-$a _ { 1 } = - 3 , a _ { n + 1 }= \sqrt { 8 + 2 a _ { n } }$
A) $- 9$
B) $- 3$
C) 8
D) 4

Question

Assume that the sequence converges and find its limit.
-$a _ { 1 } = - 3 , a _ { n  + 1 }= \sqrt { 8 + 2 a _ { n } }$
A) $- 9$
B) $- 3$
C) 8
D) 4

Quizplus · Accepted Answer

Given the sequence converges to a limit $L$, we use the recursive formula to find $L$. Setting $a_{n+1} = a_n = L$, we get $L = \sqrt{8 + 2L}$. Squaring both sides gives $L^2 = 8 + 2L$, which simplifies to $L^2 - 2L - 8 = 0$. Solving this quadratic equation, we find $L = 4$ as the positive solution that makes sense in the context of the sequence.

Assume That the Sequence Converges and Find Its Limit a1=−3,an+1=8+2ana _ { 1 } = - 3 , a _ { n + 1 }= \sqrt { 8 + 2 a _ { n } }a1​=−3,an+1​=8+2an​​

Assume That the Sequence Converges and Find Its Limit $a _ { 1 } = - 3 , a _ { n + 1 }= \sqrt { 8 + 2 a _ { n } }$