Mary extended the pattern 2 4 6 8 could be 2 4 8 16 32. Paul extended the same pattern to be 2 4 8 14 22. They asked who was correct. How should u respond

Question

A pattern of 2 4 6 8 could be 2 4 8 16 32.  Paul extended the same pattern to be 2 4 8 14 22.  They asked who was correct.  How would you respond

 

Answer 1

It's related to a sequence, a list of number written in a specific order.

Let a_n = n^th term, and n ⟩ 0 and an integer, then the pattern can be expressed in general sequence term, 

  a pattern of 2 4 6 8......,  or  a_n = 2n,  

  a pattern of 2 4 8 16 32......,   a_n = 2ⁿ, 

  a pattern 2 4 8 14 22......,  a_n = 2+n(n-1) = n² - n + 2, 

They are all sequences having their own rules.