Question

10) if the pattern indicated below is continued, what would be the total number of cubes in the 5th stage

of the pattern?
a) 55
b) 36
c) 45
d) 30

Answer 1

Option A. 55

Explanation:

From the diagram given above, we discovered that the number of cubes in each stage is simply the addition of the squares of the number from 1 to the stage number i.e

1st Stage = 1² = 1 cube

2nd Stage = 1² + 2² = 1 + 4 = 5 cubes.

3rd Stage = 1² + 2² + 3² = 1 + 4 + 9

3rd stage = 14 cubes

With the above idea in mind, we can obtain the number of cubes in the 5th stage as illustrated below:

5th stage = 1² + 2² + 3² + 4² + 5²

5th stage = 1 + 4 + 9 + 16 + 25

5th stage = 55 cubes

Thus, there are 55 cubes in the 5th stage.