Question

Stage 1: 1 = 1
Stage 2: 1+3 = 4
Stage 3: 1 +3+5 = 9
Stage 4: 1+3+5+7= 16
a. Find the next four stages and their sums.
b. What is the sum in Stage 20?
c. In what stage will the sum be 567? What is the greatest number added in the sum of this pattern? Explain.

Answer 1

Did you notice that the result is the square of the stage number?

e.g. stage 4 ---->4^2 = 16

carry on

Answer 2

For (b) and (c) you ought to know that the sum of the first n squares is

[n(n+1)(2n+1)]/6