A pile of blocks has 40 blocks in the bottom row 36 blocks in the second row 32 blocks in the third row and so on until there are only 4 blocks on the top row how many blocks? Are there in the 7th row? How many blocks are there in all
(40-4)/4 = 9
so, there are 9 rows after the 1st, making 10 in all.
On the nth row, there are
40-(n-1)*4 = 44-4n bricks
The sum of n rows, Sn, with
a = 40
d = -4
is
Sn = n/2 (2*40 - (n-1)*4) = 2n(21-n)
Now you can answer the questions.
135
We can observe that each row has 4 less blocks than the row below it.
To find out how many blocks are in the 7th row, we can use the following formula:
Number of blocks in the nth row = (First row - (n-1) * 4)
Using this formula, we can calculate the number of blocks in the 7th row:
Number of blocks in the 7th row = (40 - (7-1) * 4)
= (40 - 6 * 4)
= (40 - 24)
= 16
So, there are 16 blocks in the 7th row.
Now, to calculate the total number of blocks, we can sum up the blocks in each row. We know that each row has 4 less blocks than the row below it. So, we can use a sum of an arithmetic progression formula:
Sum of n terms = (n/2) * (First term + Last term)
Here, the first term is 40 and the last term is 4. So, we can calculate the total number of blocks as:
Total number of blocks = (7/2) * (40 + 4)
= (7/2) * 44
= 7 * 22
= 154
Therefore, there are 16 blocks in the 7th row, and the total number of blocks is 154.
To find out how many blocks are in each row and the total number of blocks, we can look for a pattern in the given information.
The pattern seems to be that each row has 4 blocks fewer than the row below it. We can calculate the number of blocks in each row by subtracting 4 from the previous row.
To find the number of blocks in the 7th row, we can start from the bottom row and subtract 4 for each row until we reach the 7th row.
40 - 4 = 36 (6th row)
36 - 4 = 32 (5th row)
32 - 4 = 28 (4th row)
28 - 4 = 24 (3rd row)
24 - 4 = 20 (2nd row)
20 - 4 = 16 (1st row)
Therefore, there are 16 blocks in the 7th row.
To find the total number of blocks, we can add up the number of blocks in each row.
40 + 36 + 32 + 28 + 24 + 20 + 16 = 196
So, there are a total of 196 blocks.