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?

The answer somehow is 36, and the total number of blocks is 576. I don't know how to get this.

Im probably supposed to use one of these formulas... Sn = n[2a +(n-1)d]/2
Sn = n(a +tn)/2. Still I don't get how to do it

the difference between the ninth and fifth is 28, so that is between 4 rows, so the differnce between each row is 28/4=7

start with 9th and go down:

92
85
78
71
64
57
50
43
36 first row.

Sum them: Sn= 9(2*36+8*7)/2=9*(72+56)/2=
Sn=9*64=576

Thanks so much. I was so confused :)

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

The formula for the nth term of an arithmetic sequence is:

an = a1 + (n-1)d

where 'an' represents the nth term, 'a1' is the first term, 'n' is the position of the term, and 'd' is the common difference between the terms.

In this case, we are given the number of animal blocks in the 5th and 9th rows, which are 64 and 92 respectively. We can use this information to set up two equations and solve for 'a1' and 'd'.

Using the first given value:
a5 = a1 + (5-1)d
64 = a1 + 4d

Using the second given value:
a9 = a1 + (9-1)d
92 = a1 + 8d

Now, we can solve these two equations simultaneously to find the values of 'a1' and 'd'.

Let's multiply the first equation by 2 and subtract the second equation from it:

128 = 2a1 + 8d
92 = a1 + 8d
-----------------
36 = a1

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

Now, to find the total number of animal blocks used in the arrangement, we can use the formula for the sum of an arithmetic sequence:

Sn = (n/2)(a1 + an)

In this case, we are given that the last row is the 9th row, with 92 animal blocks.

Using the formula:
S9 = (9/2)(a1 + 92)

Substituting the value of 'a1' we found earlier:
S9 = (9/2)(36 + 92)

Simplifying:
S9 = (9/2)(128)
S9 = 576

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

To find the number of animal blocks in the first row, you need to use the concept of an arithmetic sequence. In an arithmetic sequence, the difference between consecutive terms is constant.

To find this difference, we can subtract the number of animal blocks in the 5th row from the number of blocks in the 9th row.

Number of blocks in the 9th row - Number of blocks in the 5th row = 92 - 64 = 28

Since this difference is constant for each row, we can find the number of blocks in the first row by subtracting 4 times the difference from the number of blocks in the 5th row.

Number of blocks in the first row = Number of blocks in the 5th row - 4 * difference
= 64 - 4 * 28
= 64 - 112
= -48

However, a negative number of blocks does not make sense in this context, so we need to adjust our approach.

Since the difference between consecutive terms is constant, this means that the number of blocks increases as we move from the first row to the last row. Therefore, the first row must have fewer blocks than the 5th row.

We can adjust our method by finding the difference as the positive value and then subtracting it instead of adding it.

Number of blocks in the first row = Number of blocks in the 5th row + 4 * |difference|
= 64 + 4 * 28
= 64 + 112
= 176

Therefore, there are 176 animal blocks in the first row.

To find the total number of blocks used in the arrangement, we can use the formula for the sum of an arithmetic series:

Sn = n/2[2a + (n-1)d]

In this formula, Sn represents the sum of the first n terms, a is the first term, and d is the common difference.

In our case, the number of terms, n, is the total number of rows, which is 9. And since we know the first term, a, is 176 (from the previous calculation), and the difference, d, is 28, we can substitute these values into the formula:

Sn = 9/2[2 * 176 + (9-1) * 28]
= 9/2[352 + 8 * 28]
= 9/2[352 + 224]
= 9/2 * 576
= 9 * 288
= 2592

Therefore, the total number of animal blocks used in the arrangement is 2592.