Stairway of Blocks

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A stairway is formed by stacking even blocks next to and on top of each other. If the stairway depicted above is 5 blocks in length and 4 blocks in height, with a thin step at the beginning that does not require a block, and the stairway is only 1 block in width, how many blocks will be required to build such a stairway 20 blocks in length?

Review: Stairway of Blocks


Explanation

In this question, the length of the stairway is padded by 1, because there is a block's length at the beginning with no blocks. In terms of blocks, it's really 19 blocks long. Received that way, the first unit of length is 1 block high, the second is 2 blocks high, and so on. So the number of blocks we need is



We can find the sum of these numbers by using the average formula, since



The number of items we are adding is , as we can confirm by playing with smaller numbers, if we have to. The average therefore will be the 10th item in the list, with 9 pairs of numbers on either side that balance the different out from that item. The tenth item is 10, so that's the average, and the sum is . This is the number of blocks we need.

The correct answer is (B).


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