A theater has 15 rows of seats with 30 in the first row, 33 in the second row, 36 in the third row, and so on in the same pattern. How many TOTAL seats are in the theater?

Answer 1

Hi,

In fact it is arithmetic series,

15 rows it means n= 15

with 30 in the first row it means a = 30 same pattern it means d = 3

How many TOTAL seats it means you need to use sum formula

s = n/2 [ 2a + (n-1)d]

s = 15/2 [ 2*30 + ( 15-1) 3 ] = 765 seats

I hope it is useful,

Minoo

Answer 2

15 rows

1st row has 30

2nd has 33

3rd has 36

nth row has 30+3(n-1)

15th has 30 + 3(14) = 30+42 = 72

an = a1 +d(n-1)

an = 30 +3(n-1)

sum of n terms

s1 = 30

s2 = 30+33 = 63 = n/2(30+33) = 63

s3 = 63+36 = 99

s4 = 99+ 39 = 138 = 4/2(30+39)= 138

s5 = 138+42 = 180 = 5/2(30+42) = 5(36) = 180

s6 = 180+45 = 225 = 6/2(30+45)=225

s7 = 225+48 = 273

s8 = 273+51 = 324

s9= 324+54= 378 =

s10 = 378+57 = 435

s11 = 435+60 = 495 = 11/2(30+60) = 11/2(90)= 11(45) = 495

s12 = 495+63= 558 = 12/2(30+63) = 6(93) = 558

s13 = 558+66 = 624

s14= 624+69= 693

s15 = 693+72= 765

sn = (n/2)(a1 +an)

a1=30,

an=30+d(n-1) = 30+3(14) = 30+42 = 72

s15 =(15/2)(30+72) = (15/2)(102) = 15(51) = 765

Answer 3

First, write the pattern as a sequence

row 1 row 2 row 3

30 seats 33 seats 36 seats

Second, find the equation that makes the sequence y=mx+b

m will be the difference in the sequence numbers

b will be what you + or - to make the equation work if needed

1) difference in numbers 36-33 = 3 33-30 = 3 so the difference is 3

2) y=3x

Check y=3(1) the first number in sequence is supposed to be 30 but 3(1) is just 3 so the equation is not right yet

3) + or - to make it work y=3x+27

check y=3(2)+27 the second number is supposed to be 33 3(2)+27 = 33 so equation works

Now, you want the 15th row so substitute 15 into the equation to find the amount of seats.