Question

A theater has 20 rows of chairs. The first row has 16 chairs, the second has 18, the third has 20, and so on. In total, the theater seats _____ people.

****So I think the pattern is add 2 for each row.... But idk how to solve it... is there like an equation or something???

Answer 1

Hi!! Thanks for coming to help!! :) Do you understand this? ;)

Answer 2

You have the sequence:

16, 18, 20, 22, 24, ...

You want to add up the terms:

16+18+20+22+24+...(Twentieth Term)

You can use the formula

Sn = n*(a1 + an)/2

where n is the number of terms, a1 is the first term and an is the nth term

Answer 3

ohhhh, so i forgot though, what is the n mean?? is that 20?? since there are 20 rows?

Answer 4

n = 20, yes

Answer 5

Also remember that

an = a1+ (n-1)*d

where d is the common difference

Answer 6

so a20=(16)+(20-1)(2) is that right so far?

Answer 7

yes

Answer 8

so i get 54??

Answer 9

now plug this into the formula

Sn = n*(a1 + an)/2

S20 = 20*(16 + 54)/2

...

Answer 10

so this was the first formula you listed right?

Answer 11

yes it is

Answer 12

And i get (20)(70)/2 which equals 1400/2 which = 700 ???

Answer 13

you nailed it

Answer 14

If you want to do it the long way, then list out the first 20 terms:


16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54


Then add them up


16+18+20+22+24+26+28+30+32+34+36+38+40+42+44+46+48+50+52+54 = 700


So we get the same answer

Answer 15

yay!!! :) Thanks so much @jim_thompson5910 !!! you rock!! :) oh sooo i can do it both ways and i get the same answer?

Answer 16

either way works, the formula is the best and easiest way, but it's good to know the formula works (by confirming it with the long way)

Answer 17

oh okay!! That's good to know :) Thank you!! :)

Answer 18

yw