Suppose you have a sequence that begins {2, 5, 10, 17}. Give the next 3 numbers in your sequence. Use a positional definition to define your sequence.

Question

Need help solving. I really am having a hard time understanding how to writ in positional for.

Answer 1

2 = 1 + 1 = 1²+1

 

5 = 4 + 1 = 2² + 1

 

10 = 9 + 1 = 3² + 1

 

17 = 16 + 1 = 4² + 1, etc

 

General term:  a_n = n² + 1

 

Next 3 terms:  26, 37, 50