Learning Resources

Investigation 1: Number Patterns that Grow, Part 1

Test yourself (Answers)

Use the sequence { 2 , 3.5 , 5 , 6.5 , ...} to answer the following questions:

1. t₂ - t₁ = 3.5 - 2 = 1.5
   t₃ - t₂ = 5 - 3.5 = 1.5
   t₄ - t₃ = 6.5 - 5 = 1.5
   Since there is a common difference of 1.5, the sequence is arithmetic.
   
   
2. The function rule for the n^th term of the sequence is:
                   t_n = 2 + (n - 1) x 1.5
                   t_n = 2 + 1.5n - 1.5
                   t_n = 1.5n +0.5
   
   The 25^th term is :  t₂₅ = 1.5(25) +0.5 = 37.5 + 0.5 = 38
   
   
   
3.      
   
   The slope of the function is 1.5 and this is also the common difference.