https://file.aiquickdraw.com/mathbot/file/1727020871672ezc0eaf4.jpg

The problem in the image describes a decreasing number of blocks per row, starting with 87 blocks in the bottom row, and reducing the number of blocks by 6 in each successive row, with the top row containing 3 blocks. 

This forms an arithmetic sequence where:

- First term (\(a_1\)) = 87
- Common difference (\(d\)) = -6
- Last term (\(a_n\)) = 3

We can solve the following two questions:
1. How many rows are there in the pile?
2. What is the total number of blocks in the pile?

Let me solve these step-by-step:

### 1. **Number of Rows:**

In an arithmetic sequence, the general term formula is:
\[
a_n = a_1 + (n-1) \cdot d
\]
We know \(a_1 = 87\), \(d = -6\), and \(a_n = 3\). Plugging these into the formula:
\[
3 = 87 + (n-1) \cdot (-6)
\]
Simplifying this equation:
\[
3 = 87 - 6(n-1)
\]
\[
3 = 87 - 6n + 6
\]
\[
3 = 93 - 6n
\]
\[
6n = 93 - 3
\]
\[
6n = 90
\]
\[
n = \frac{90}{6} = 15
\]
So, there are **15 rows** in total.

### 2. **Total Number of Blocks:**

The sum of an arithmetic sequence is given by:
\[
S_n = \frac{n}{2} \cdot (a_1 + a_n)
\]
Substituting the known values:
\[
S_{15} = \frac{15}{2} \cdot (87 + 3)
\]
\[
S_{15} = \frac{15}{2} \cdot 90
\]
\[
S_{15} = 15 \cdot 45 = 675
\]
So, the total number of blocks is **675**.

Would you like further details or have any questions? Here are 5 related questions to think about:
1. What happens if the common difference was different, say -4 instead of -6?
2. How would the sum change if the top row had more than 3 blocks, like 5 blocks?
3. Can you derive a formula for the number of rows based on the common difference and the top row value?
4. What real-world structures could use this type of block arrangement?
5. How could you find the average number of blocks per row?

**Tip:** For arithmetic sequences, always check if the pattern is consistent and use the general term formula to make predictions.

A pile of blocks has 87 blocks in the bottom row, 81 blocks in the 2nd row, 75 blocks in the 3rd row, and so on until there are only 3 blocks on the top row. How many rows are there, and what is the total number of blocks?

Solve how many rows and the total number of blocks in a pyramid-like arrangement, where the number of blocks decreases by 6 in each row starting from 87 blocks in the first row and ending with 3 blocks at the top. Includes arithmetic sequence formulas.

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