Suppose you have a sequence that begins {3, 7, 11, 15}. Give the next 3 numbers in your sequence. Use a positional definition to define your sequence

Question

Having trouble writing the problem in positional form.

Answer 1

The first differences are a constant 4 which means that his is an arithmetic sequence the next terms of which are 19, 23, 27.  The general term of this sequence is a_n = 3 + (n-1)4 where nis is an integer greater than of equal to 1.

 

Whenever the first differences of a sequence are constant the sequence is an arithmetic sequence.