Check my answer please!
A tower of blocks has 1 block in the top row, 3 blocks in the next row, 5 blocks in the next row, and so on. there are six rows in all. how many blocks are in the tower?
11 blocks
47 blocks
36 blocks *MY ANSWER*
49 blocks
11 blocks is my new answer
should have stayed with 36
1+3+5+7+9+11 = 36
In fact, if you add up the first n odd numbers, the sum is n^2.
How did you decide on 11? 1+3+5=9 and you still had three rows to go.
To find the number of blocks in the tower, you can calculate the sum of blocks in each row.
In this tower, the number of blocks in each row forms an arithmetic sequence with a common difference of 2. The first term is 1, the second term is 3, and so on.
To find the last term of the sequence, you can use the formula for the nth term of an arithmetic sequence:
nth term = first term + (n - 1) * common difference.
In this case, the nth term is 5 (since there are six rows), the first term is 1, and the common difference is 2. Substituting these values into the formula, we get:
5 = 1 + (6 - 1) * 2
5 = 1 + 5 * 2
5 = 1 + 10
5 = 11
Now, to find the sum of the arithmetic sequence (the number of blocks in the tower), you can use the formula for the sum of an arithmetic sequence:
sum = (number of terms / 2) * (first term + last term).
In this case, the number of terms is 6, the first term is 1, and the last term is 11. Substituting these values into the formula, we get:
sum = (6 / 2) * (1 + 11)
sum = 3 * 12
sum = 36.
Therefore, the correct answer is 36 blocks.