A child organizes animal blocks in rows on the ground. There are 64 animal blocks in the 5th row & 92 of those blocks in the 9th and last row. Suppose that the number of animal blocks frm row to row form an arithmetic sequence.

The number of animal blocks in the first row is....

I can’t seem to find a pattern, having a hard time solving this problem too.
Also How do I find the total number of blocks used in the arrangement?

To find the number of animal blocks in the first row, we need to determine the common difference in the arithmetic sequence.

First, let's find the number of animal blocks between the 5th and the 9th row. We know that there are 64 animal blocks in the 5th row and 92 animal blocks in the 9th row.

The difference in the number of animal blocks between the 5th and 9th row is (92 - 64) = 28.

Since the number of animal blocks between each row forms an arithmetic sequence, we can divide this difference by the number of rows between the 5th and the 9th row. In this case, it is (9 - 5) = 4.

So, the common difference in the arithmetic sequence is 28/4 = 7.

Now, to find the number of animal blocks in the first row, we can subtract the common difference multiplied by the number of rows between the 5th row and the first row from the number of animal blocks in the 5th row.

The number of rows between the 5th row and the first row is (5 - 1) = 4.

Therefore, the number of animal blocks in the first row is 64 - (7 * 4) = 64 - 28 = 36.

So, there are 36 animal blocks in the first row.

To find the total number of blocks used in the arrangement, we can use the formula for finding the sum of an arithmetic sequence. The formula is: S = (n/2) * (2a + (n-1)d)

Where:
S = total sum,
n = number of terms in the sequence,
a = first term,
d = common difference.

In this case, we know that the last row is the 9th row, so n = 9. We also know the first term, a (which is the number of blocks in the first row) is 36, and the common difference, d, is 7.

Using the formula, we can calculate the total sum: S = (9/2) * (2 * 36 + (9-1) * 7) = 4.5 * (72 + 56) = 4.5 * 128 = 576.

Therefore, the total number of blocks used in the arrangement is 576.