Question

A theater has 31 rows of seats. The first row has 24 ​seats, the second row has 27 ​seats, the third row has 30 ​seats, and so on. How many seats are in the​ theater?

I neeeed help

Answer 1

2,139 seats

Explanation:

the seats increase by 3 every row so I'm going to make a chart to show you how much the seats increase to 31 rows then add all off them to find total.

1 : 24

2: 27

3 : 30

4 : 33

5 : 36

6 : 39

7 : 42

8 : 45

9 : 48

10 : 51

11 : 54

12 : 57

13 : 60

14 : 63

15 : 66

16 : 69

17 : 72

18 : 75

19 : 78

20 : 81

21 : 84

22 : 87

23 : 90

24 : 93

25 : 96

26 : 99

27 : 102

28 : 105

29 : 108

30 : 111

31: 114

You can see from the chart that the number of seats increases by 3 for each row, starting from 24 seats in the first row and ending with 114 seats in the 31st row. To find the total number of seats, you can add up all the numbers in the chart:

24 + 27 + 30 + 33 + ... + 111 + 114

This is an arithmetic series with a first term of 24, a common difference of 3, and 31 terms. You can use the formula for the sum of an arithmetic series to find the total:

Sum = n/2 * (a + l)

where n is the number of terms, a is the first term, and l is the last term.

n = 31, a = 24, and l = 114, so you can substitute these values into the formula and simplify:

Sum = 31/2 * (24 + 114)

Sum = 15.5 * 138

Sum = 2139

Therefore, the theater has a total of 2,139 seats, which agrees with the result obtained earlier.

Answer 2

2139 seats

Explanation:

24,27,30,.......

n = 31

This forms an arithmetic series. Sum of arithmetic series will give the number of seats in the theater.

a = first term = 24

d = difference = second term - first term

= 27 - 24

= 3

`\sf \boxed{S_n=(n)/(2)[2a+(n-1)*d]}`

`=(31)/(2)[2*24+30*3]\\\\=(31)/(2)[48+90]\\\\=(31)/(2)*138\\\\=31*69\\\\=2139`