Answer to Question #350549 in Algebra for Hangwy

Question

Draw a diagram by which you can visually explain to learners in the Intermediate Phase why the sum of five consecutive numbers is equal to the fifth multiple of the middle number. Choose any set of five consecutive numbers to illustrate your statement. Write down your explanation in four powerful sentences.

Answer 1

The sum of the first and fifth digits of 5 consecutive numbers is twice the sum of the third digit. Similarly, the sum of the second and fourth digits is twice the number of the third digit. Thus, the sum of the five consecutive digits is five times the sum of the third digit:

1+5 = 6 = 2 * 3

2+4 = 6 = 2 * 3

3 = 1 * 3

3 * (2+2+1) = 3 * 5