Question

Mark is building a pyramid out of blocks. The top of his pyramid has 1 block, the second layer has 4 blocks, the third layer has 9 blocks, the fourth layer has 16 blocks, and the fifth layer has 25 blocks. If Mark decided to add a sixth layer to his pyramid, how many blocks would that layer have?

Answer 1

The number of blocks in sixth layer would be 36.

Explanation:

The number of blocks from the top layer to the fifth layer are:
`1, 4, 9, 16, 25`

The difference between the consecutive numbers are....

`4-1=3\\ \\ 9-4=5\\ \\ 16-9=7\\ \\ 25-16=9`

These differences make an arithmetic sequence as
`3, 5, 7, 9,....` with common difference of
`2`.

That means, the next term in this arithmetic sequence will be:
`9+2=11`

So, the sixth layer will have
`11` more blocks than the fifth layer.

Thus, the number of blocks in sixth layer
`= 25+11= 36`

Answer 2

36

Explanation:

The difference between the first and second layer is 3, then 5, then 7, then 9, so you can deduce the next one will be 11.

25+11=36