arithmetic sequence real life problems
TRANSCRIPT
SITUATION:
SITUATION:There are 125 passengers in
the first carriage, 150 passengers in the second carriage and 175 passengers
in the third carriage, and so on in an arithmetic sequence.
PROBLEM:What’s the total number of passengers in the
first 7 carriages?
SOLUTION:The sequence is 125, 150, 175 …
Given: a1= 125; a2= 150; a3= 175
Find: S7=?
an = 125+ (n-1)25a7 = 125+(7-
1)25=275
We can use the formula:
Thus, =1400
Carriage 1st 2nd
3rd
… 7th
First 7 carriages
Number of Passengers
125
150
175
… ? Sn
SITUATION:
SITUATION:There are 130 students in grade
one, 210 students in grade two and 290students in grade three in a primary school, and so on in an
arithmetic sequence.
PROBLEM:What’s the total amount of students
In the primary school?(Primary School has 6 grades)
SOLUTION:The sequence is 130, 210, 290 …
Given: a1= 130; a2= 210; a3= 290Find: S6= ?
an = 130+(n-1)80a6 = 130+(6-1)80=530
We can use the formula:
Thus, = 1980
Grade 1st 2nd 3rd … 6th Total from 1st to 6th Grade
Number of Students
130
210 290 … ? Sn
SITUATION:
A car travels 300 m the first minute, 420 m the next minute,
540 m the third minute, and so on in an arithmetic
sequence.
PROBLEM:What’s the total distance the car travels in
5 minutes?
SOLUTION:The sequence is 300, 420, 540 …
Given: a1= 300; a2= 420; a3= 540Find: S5= ?
an = 300+(n-1)120a5 = 300+(5-1)120=780
We can use the formula:
Thus, = 2700
Minute First Second Third Fourth Fifth 5 minutes in Total
Distance 300 420 540 … ? Sn
PROBLEM:
SITUATION: A writer wrote 890 words on the
first day, 760 words on the second day and 630 words on the third day, and so on in an arithmetic sequence.
PROBLEM:How many words did the writer
write in a week?
SOLUTION:The sequence is 890, 760, 630 …
Given: a1= 890; a2= 760; a3= 630Find: s7= ?
an = 890-(n-1)130a7 = 890-(7-1)130=110
We can use the formula:
Thus, =3500
Day 1st 2nd 3rd … 7th Whole Week
Number of Words
890
760 630 … ? Sn
SITUATION:
You visit the Grand Canyon anddrop a penny off the edge of a cliff.
The distance the penny will fall is 16 feet the first second, 48 feet the
next second, 80 feet the third second, and so on in an
arithmetic sequence.
PROBLEM:What is the total distance the object will fall
in 6 seconds?
SOLUTION:Arithmetic sequence: 16, 48, 80, ...
Given: a1= 16; a2= 48; a3= 80Find: S6= ?
The 6th term is 176.
Now, we are ready to find the sum:
Second 1 2 3 4 5 6 Total distance in 6 seconds
Distance 16 48 80 … … 176 .....
SITUATION:The sum of the interior angles
of a triangle is 180º,of a quadrilateral is 360º
and of a pentagon is 540º.
PROBLEM:Assuming this pattern continues,
find the sum of theinterior angles of a dodecagon (12 sides).
SOLUTION:Given: d=180
Find: a10= ?
This sequence is arithmetic and the common difference
is 180. The 12-sided figure will be the 10th term in
this sequence. Find the 10th term.
180 360 540 ... ?
Sides: 3 4 5 ... 12
Term: 1 2 3 ... ?
SITUATION:After knee surgery, your trainer tells you toreturn to your jogging program slowly. He suggests jogging for 12 minutes each day
for the first week.Each week thereafter, he suggests that you
increase that time by 6 minutes per day.
PROBLEM:How many weeks will it be before you are upto jogging 60 minutes per day?
SOLUTION:Given: a1 60; d=6
Find: n= ?
Adding 6 minutes to the weekly jogging time for each week creates the
sequence: 12, 18, 24, ...This sequence is arithmetic.
Week Number
1 2 3 … ?
Minutes of Jogging each day inside the week
12 18 24 … n
SITUATION:20 people live on the first floor of
the building, 34 people on the second floor and 48 people on the
third floor, and soon in an arithmetic sequence.
PROBLEM:What’s the total number of people living in
the building?
SOLUTION:The sequence is 20, 34, 48 …
Given: a1= 20; a2= 34; a3= 48Find: S5= ?
Floor 1st 2nd 3rd 4th 5th People living in the building
Number of People who live
20 34 48 … ? Sn
an = 20+(n-1)14a5 = 20+(5-1)14=76
We can use the formula:
Thus, =240
SITUATION:Lee earned $240 in the first week, $350in the second week and $460
in the third week, and so on in an arithmetic
sequence.
PROBLEM:How much did he earn in the first 5 weeks?
SOLUTION:The sequence is 240, 350, 460 …
Given: a1= 240; a2= 350; a3= 460
Find: S5= ?Week 1st 2nd 3rd 4t
h5th
First 5 weeks
Money that Lee Earned
$240
$350
$460
… ? Sn
an=240+(n-1)110a5=240+(5-1)110=680
We can use the formula:
Thus, =2300
SITUATION:An auditorium has 20 seats on
the first row, 24 seats on the second row, 28
seats on the third row, and so on and has30 rows of seats
PROBLEM:How many seats are in the theatre?
SOLUTION:Given: a1= 20; a2= 24; a3= 28; n=30
Find: S30= ?
Row 1st 2nd 3rd … 30th Total number of rows
Number of seats
20 24 28 … ? Sn
To find a30 we need the formula for the sequence and then substitute n = 30. The formula for an arithmetic sequence is
We already know that is a1 = 20, n = 30, and the common difference, d, is 4. So now we have
So we now know that there are 136 seats on the 30th row. We can use this back in our formula
for the arithmetic series.