Assume that the sequence converges and find its limit.
-$$a _ { 1 } = 5 , a _ { n + 1} = \sqrt { 5 a _ { n } }$$
A) $- 5$
B) 1
C) 5
D) 25

Question

Quizplus · Accepted Answer

We can start by finding the first few terms of the sequence:
$a_1=5$
$a_2=\sqrt{5a_1}=\sqrt{25}=5$
$a_3=\sqrt{5a_2}=\sqrt{125}=5\sqrt{5}$
$a_4=\sqrt{5a_3}=5$
We notice that after the second term, every term is equal to 5. Thus, the limit of the sequence is 5.

Assume That the Sequence Converges and Find Its Limit a1=5,an+1=5ana _ { 1 } = 5 , a _ { n + 1} = \sqrt { 5 a _ { n } }a1​=5,an+1​=5an​​

Assume That the Sequence Converges and Find Its Limit $a _ { 1 } = 5 , a _ { n + 1} = \sqrt { 5 a _ { n } }$