Patterns and sequences

Finding consecutive counting numbers

Introduction
All counting numbers are got by adding 1, 2, 3, 4 consecutively to the first number


Examples
The sum of three consecutive counting numbers is 36. What are these numbers?
Let the 1st counting number be k
1st = (k)
2nd = (k+1)
3rd = (k +2)
(k) + (k+1) +(k+2) = 36
k + k + 1 + k +2 = 36
k + k + k + 1 + 2 = 36
3k + 3 = 36

image 12
image 13

Therefore K = 11


Activity

  1. The sum of 3 consecutive counting numbers is 21. What are the numbers?
  2. Find the three consecutive counting numbers whose mean is 39
  3. List the four consecutive counting numbers whose total is 86
  4. Find 3 consecutive counting numbers whose sum is 51
  5. List 3 consecutive counting members whose total is 72
  6. The sum of three consecutive counting numbers is 93. What are the numbers?