A pile of bricks has 85 bricks in the bottom row, 81 bricks in the second row up, 77 in the third, and so on up to the top row that contains only 1 brick. How many bricks are in the 12th row?
I don't know if I'm right but I attempted this problem below
c = a1 - d
c = 85 - 4 = 81
- 85 + 81 = 166
Sn = n / 2 (a1 + an)
Sn = 85 / 2 (85 + 166)
Sn = 10667.5
I can't follow you calculation.
Row 1 has
85
Row 2 has
81
row 3 has
77
The nth row will have
85-4(n-1)
so if n=12
then
85-4(12-1)=85-44=41 bricks
Right, instead of using the Sn formula. I could have just use an = a1 + (n - 1) d
Thanks a lot
To find the number of bricks in the 12th row, you can use the arithmetic sequence formula. In this case, the first term (a1) is 85, the common difference (d) is -4, and the number of terms (n) is 12.
The formula for the nth term (an) of an arithmetic sequence is:
an = a1 + (n - 1) * d
Using this formula, we can calculate the number of bricks in the 12th row:
a12 = 85 + (12 - 1) * -4
= 85 + 11 * -4
= 85 + (-44)
= 41
Therefore, there are 41 bricks in the 12th row.
To find the number of bricks in the 12th row, you can use the formula for the sum of an arithmetic series, which is Sn = n/2 (a1 + an), where Sn is the sum of the series, a1 is the first term, an is the nth term, and n is the number of terms.
In this case, the first term (a1) is 85 bricks, and the common difference (d) between each row is 4 (since each row has 4 fewer bricks than the previous row).
To find the 12th term (an), you can use the formula for the nth term of an arithmetic sequence: an = a1 + (n - 1) * d. Plugging in the values, we have an = 85 + (12 - 1) * 4 = 85 + 44 = 129.
Now, you can substitute these values into the formula for Sn: Sn = 12/2 (85 + 129) = 6 * (85 + 129) = 6 * 214 = 1284.
Therefore, there are 1284 bricks in the 12th row.