PLEASE I REALLY NEED HELP WITH THIS
The seats at a local baseball stadium are arranged so that each row has five more seats than the row in front of it. If there are four seats in the first row, how many total seats are in the first 24 rows?
To find the total number of seats in the first 24 rows, we need to calculate the number of seats in each row and sum them up.
Given that there are four seats in the first row, we can find the number of seats in each subsequent row by adding five seats to the previous row.
Let's break it down step by step:
1. Calculate the number of seats in each row:
- First row: 4 seats
- Second row: 4 + 5 = 9 seats
- Third row: 9 + 5 = 14 seats
- Fourth row: 14 + 5 = 19 seats
- Fifth row: 19 + 5 = 24 seats
- ...
- 24th row: ?
2. Continue the pattern to find the number of seats in the 24th row:
- The number of seats in the nth row can be found using the formula: 4 + (n-1)*5
- For the 24th row, n = 24
- 24th row: 4 + (24-1)*5 = 4 + 23*5 = 4 + 115 = 119 seats
3. Calculate the total number of seats in the first 24 rows:
- Sum up the number of seats in each row from the first row to the 24th row:
- Total seats = 4 + 9 + 14 + 19 + ... + 119
To calculate the sum of an arithmetic series (the seats in each row form an arithmetic series), you can use the formula for the sum of an arithmetic series:
- Sum = (first term + last term) * number of terms / 2
In this case, the first term is 4, the last term is 119, and the number of terms is 24. Plug in these values into the formula:
- Total seats = (4 + 119) * 24 / 2 = 123 * 12 = 1476
Therefore, the total number of seats in the first 24 rows is 1476.
To find the total number of seats in the first 24 rows, we need to determine the number of seats in each row and then sum them up.
We know that the first row has 4 seats. The row directly after it has 5 more seats, so the second row has 4 + 5 = 9 seats.
To find the number of seats in each subsequent row, we can add 5 to the number of seats in the previous row. So, the third row has 9 + 5 = 14 seats, the fourth row has 14 + 5 = 19 seats, and so on.
We can see that each row has 5 more seats than the row before it. This means that the number of seats in each row can be represented by an arithmetic sequence, where the first term is 4 and the common difference is 5.
To find the number of seats in the 24th row, we can use the arithmetic sequence formula, which is a(n) = a(1) + (n-1)d, where a(n) represents the nth term, a(1) represents the first term, n represents the number of terms, and d represents the common difference.
Plugging in the values, we have a(24) = 4 + (24-1)5 = 4 + 23*5 = 4 + 115 = 119.
So, the 24th row has 119 seats.
To find the total number of seats in the first 24 rows, we need to sum up the number of seats in each row from the first row to the 24th row.
We can use the arithmetic series formula, which is S(n) = (n/2)(a(1) + a(n)), where S(n) represents the sum of the first n terms.
Plugging in the values, we have S(24) = (24/2)(4 + 119) = 12 * 123 = 1476.
So, the total number of seats in the first 24 rows is 1476.
it is an arithmetic series, with distance 5, and you want the sum of n=24 rows.
Sum=n/2 (a1+an)
where an=a1+d(n-1)
an=4+5(23)=119 check that
sum=24/2 (123)=12*123
check all that. http://www.purplemath.com/modules/series4.htm