How many blocks are needed to build a stair step pattern that has a base of 10, a height of 10, and where each step is one block high and one block deep?
looks like you just want the sum of all the numbers from 1 to 10.
If you list the numbers, you get
1 2 3 4 ... 8 9 10
Now pair them up, starting from the ends. Each pair adds up to 11. There are 10 numbers, so 5 pairs, adding up to 11*5 = 55
Since it looks like you are going to come up against this again, note that if you add up the first n numbers, the sum is
n(n+1)/2
To determine the number of blocks needed to build a stair step pattern, we can use some basic math and the concept of arithmetic progression.
In this case, we have a base of 10 blocks and a height of 10 steps, where each step is one block high and one block deep.
To find the number of blocks needed, we need to calculate the sum of the arithmetic progression representing the number of blocks in each step. The formula for the sum of an arithmetic progression is given by:
Sum = (n/2) * (2a + (n-1)d)
In this formula:
- n represents the number of terms in the arithmetic progression, which is equal to the height of the stair pattern (10 steps in this case).
- a represents the first term of the arithmetic progression, which is 1 block in this case (since each step is one block high).
- d represents the common difference between the terms of the arithmetic progression, which is also 1 block (since each step is one block deep).
Now, let's substitute these values into the formula and calculate the sum:
Sum = (10/2) * (2*1 + (10-1)*1)
= 5 * (2 + 9)
= 5 * 11
= 55
Therefore, you would need a total of 55 blocks to build a stair step pattern with a base of 10, a height of 10, and where each step is one block high and one block deep.