Determine whether the nonincreasing sequence converges or diverges.
-$$a _ { 1 } = 1 , a _ { n + 1 } = 4 a _ { n } - 7$$
A) Converges
B) Diverges

Question

Quizplus · Accepted Answer

The sequence defined by $a_{n+1} = 4a_n - 7$ diverges. This can be seen by examining the recursive formula: each term is generated by multiplying the previous term by 4 and then subtracting 7. If we start with $a_1 = 1$, the sequence progresses as follows: $a_2 = 4(1) - 7 = -3$, $a_3 = 4(-3) - 7 = -19$, and so on. The magnitude of the terms increases without bound as $n$ increases, indicating that the sequence does not approach a finite limit, hence it diverges.

Determine Whether the Nonincreasing Sequence Converges or Diverges a1=1,an+1=4an−7a _ { 1 } = 1 , a _ { n + 1 } = 4 a _ { n } - 7a1​=1,an+1​=4an​−7

Determine Whether the Nonincreasing Sequence Converges or Diverges $a _ { 1 } = 1 , a _ { n + 1 } = 4 a _ { n } - 7$