Question

For each of the sequences below, answer the following questions:
Is the sequence bounded? (yes or no)
Is the sequence monotone? (yes or no, increasing or decreasing)
Does the sequence converge or diverge?
If the sequence converges, find the limit.

1. a1=1, an+1=−4an  for n≥1a1=1,an+1=−4an for n≥1 
   
   
2. an=1n√an=1n 
   
   
3. an=(−1)nan=(−1)n 
   
   
4. {1,−14,116,−164,…}{1,−14,116,−164,…} 
   
   
5. an=2nan=2n