How to make pyramid pattern of 140 blocks?
how about a 7-layer pyramid, with each layer 1 block wider than the layer above? Start with just 1 block on top.
To make a pyramid pattern of 140 blocks, we need to determine the number of rows and columns required.
First, we need to find a number N such that the sum of the first N natural numbers (1 + 2 + 3 + ... + N) is less than or equal to 140. This will give us the number of rows in our pyramid.
To find N, we can use the formula for the sum of an arithmetic series: S = (N/2) * (first term + last term). In this case, the first term is 1 and the last term is N. So, we have:
140 = (N/2) * (1 + N)
Simplifying the equation, we get:
140 = (N^2 + N) / 2
Multiplying both sides by 2, we get:
280 = N^2 + N
Rearranging the equation, we have:
N^2 + N - 280 = 0
Now, we can solve this quadratic equation to find the value of N. By factoring or using the quadratic formula, we get:
N = -20 or N = 14
Since the number of rows cannot be negative, N = 14. This means our pyramid will have 14 rows.
To determine the number of columns in each row, we need to find the total number of blocks in the bottom row. This can be calculated by finding the sum of the first 14 natural numbers:
Total blocks = 14 * (14 + 1) / 2 = 7 * 15 = 105
Therefore, the bottom row of the pyramid will have 105 blocks. Each row above the bottom row will have one less block than the row below it. So, the second-to-bottom row will have 104 blocks, the third-to-bottom row will have 103 blocks, and so on.
To create the pyramid pattern, we can use nested loops in a programming language like Python. Here's an example code snippet that accomplishes this:
```python
rows = 14
blocks = 105
for i in range(rows):
for j in range(blocks):
print("#", end=" ")
print()
blocks -= 1
```
In this code, the outer loop iterates over the rows, while the inner loop prints the desired number of blocks per row, and decreases the block count by 1 for each subsequent row. The `print("#", end=" ")` statement prints a block without moving to the next line.
When executing this code, it will print out the pyramid pattern of 140 blocks, with each row having one less block than the row below it.