Sangeetha Pulapaka
  1. Step 4 of  PATTERN A has 12 dots, this is because every step has an increase of 3 dots. Step 4 of  PATTERN B has 12 dots, because the dots in every step is the square of the step number and  3. For example step 0 is 0^{2}+3or 3 dots , step 1 is 1^{2}+3 or 4 dots, step 2 is 2^{2}+3 or 7 dots, step 3 is 3^{2}+3 or 12 dots.
  2. Pattern B shows a quadratic relationship, between the step number and the number of dots, because the number of dots are got by squaring the step number and adding it with 3.

Please note this question has been changed. Here is the solution for the exact same question from Kendall and Hunt.