Question

plz help
A new resturant opens in town. The first night 100 people came. For each successful night mfor a month 20more people showed up. How many poeple showed up on the 7th night?

Answer 1

@dmezzullo
@radar

Answer 2

@uri

Answer 3

@phi

Answer 4

i have to use the arithmetic series

Answer 5

you could write down a few terms.
100, 120, 140,...
in fact we could write down the number for all 7 nights, and get the answer that way.

but if you have a series, there is a formula to find the 7th term
do you know the formula?

Answer 6

you could write down a few terms.
100, 120, 140,...
in fact we could write down the number for all 7 nights, and get the answer that way.

but if you have a series, there is a formula to find the 7th term
do you know the formula?

Answer 7

you really could

Answer 8

the formula is sn[2a1+(n-1)d)]

Answer 9

that looks peculiar

how about this
http://www.regentsprep.org/Regents/math/algtrig/ATP2/ArithSeq.htm

Answer 10

you want the formula for the "nth term"
not the sum of the terms

Answer 11

yes thw nthg term

Answer 12

the*

Answer 13

and a formula has an = sign in it.

Can you write down the formula for the nth term ?

Answer 14

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

Answer 15

sn=n/2(a1+an)

is the sum of the n terms. ( sn is short for SUM of n terms)
it would give you 100+120+140+...

but the question asks for
How many poeple showed up on the 7th night

they want just the number of people that showed up on that night.

so you want the formula for the "nth term" (n will be 7 for this problem)
see the left-hand box in
http://www.regentsprep.org/Regents/math/algtrig/ATP2/ArithSeq.htm

Answer 16

ok thanks

Answer 17

The formula you want is
\[ a_n = a_1 + (n-1)d \]

d is the difference between 2 terms. Do you know what d is?
a1 is the first term. They tell you it is 100

can you find a7 ?

Answer 18

i got 220

Answer 19

Let's see:
d= 20 (they tell us this)
a1=100 (they tell us this)
n= 7

an= a1 + (n-1)*d
replace the letters with numbers:

a7= 100 + (7-1)*20
a7= 100+6*20 = 100+120= 220

yes, the 7th term is 220.
as a check, we can do it the hard way:
100 <-- 1st day
120
140
160
180
200
220 <-- 7th day