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?

IN RECTANGLE ABCD POINTS J,K,L, AND M ARE THE MID-POINTS OF SIDES AB,BC,CD AND DA RESPECTIVELY AB=24 CM AND AD=10CM . I NEED A ANSWER

700-284=?

To find the number of animal blocks in the first row, we can use the formula for an arithmetic sequence.

In an arithmetic sequence, each term is equal to the previous term plus a common difference. Let's assume that the common difference is 'd'.

The formula to find the nth term (in this case, the number of animal blocks in the nth row) of an arithmetic sequence is given by:

an = a1 + (n - 1)d

Where:
an is the nth term
a1 is the first term
n is the term number
d is the common difference

Now, we know that in the 5th row there are 64 blocks. So, we can substitute these values:

64 = a1 + (5 - 1)d

Simplifying this equation gives:

64 = a1 + 4d

Similarly, in the 9th (and last) row, there are 92 blocks:

92 = a1 + (9 - 1)d
92 = a1 + 8d

Now, we have a system of two equations:

64 = a1 + 4d
92 = a1 + 8d

To solve this system, we can subtract the first equation from the second equation:

92 - 64 = (a1 + 8d) - (a1 + 4d)

28 = 4d

Simplifying further:

7 = d

Now, substitute the value of d into one of the original equations, let's use the first equation:

64 = a1 + 4(7)
64 = a1 + 28
a1 = 64 - 28
a1 = 36

So, the number of animal blocks in the first row is 36.

To find the total number of blocks used in the arrangement, we need to find the sum of the arithmetic sequence. The formula to find the sum of an arithmetic sequence is:

Sn = (n/2)(2a1 + (n - 1)d)

Where:
Sn is the sum of the first 'n' terms of the sequence

In this case, we have 9 rows, so n = 9. Substituting the known values into the formula:

S9 = (9/2)(2(36) + (9 - 1)(7))
S9 = (9/2)(72 + 8 * 7)
S9 = (9/2)(72 + 56)
S9 = (9/2)(128)
S9 = (9 * 128)/2
S9 = 1152/2
S9 = 576

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