Suppose you have a sequence that begins {2, 7, 17, 37}. Give the next 3 numbers in your sequence. Use a recursive definition to define your sequence.

Question

Can I have a break down on how to get the answer. For example use.

Answer 1

The first differences of this sequence are 5, 10, & 20, i.e. Δu_n = 5*2^n-1 and the next terms are 77, 167, & 327

and u_n+1 = u_n + 5*2^n-1 where u₁ = 2  and n is a positive integer greater than of equal to 1.

 

The general term for the sequence is u_k = 2 +5 (2^k -1) for n an integer greater than or equal to 0!