Arithmetic Sequence Real Life Problems

A sample document about examples of real life problems about "Arithmetic Sequence" in Mathematics 10

1. 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.

2. 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)25
a7 = 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

3. 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.

4. 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= 290
Find: S6= ?








an = 130+(n-1)80
a6 = 130+(6-1)80=530

We can use the formula:
Thus, = 1980







Grade 1st 2nd 3rd … 6th Total
from 1
st

to 6
th

Grade
Number
of
Students
130 210 290 … ? Sn

5. 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.

6. 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= 540
Find: S5= ?






an = 300+(n-1)120
a5 = 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

7. 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.

8. PROBLEM:
How many words did the writer
write in a week?

SOLUTION:
The sequence is 890, 760, 630 …

Given: a1= 890; a2= 760; a3= 630
Find: s7= ?





an = 890-(n-1)130
a7 = 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

9. SITUATION:

You visit the Grand Canyon and
drop 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.

10. 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= 80
Find: S6= ?


The 6
th
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 .....

11. SITUATION:
The sum of the interior angles
of a triangle is 180º,of a
quadrilateral is 360º
and of a pentagon
is 540º.

12. PROBLEM:
Assuming this pattern continues,
find the sum of the
interior 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 10
th term in
this sequence. Find the 10
th term.




180 360 540 ... ?
Sides: 3 4 5 ... 12
Term: 1 2 3 ... ?

13. SITUATION:
After knee surgery, your trainer tells you to
return 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.

14. 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

15. 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.

16. 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= 48
Find: 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)14
a5 = 20+(5-1)14=76

We can use the formula:
Thus, =240

17. 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.

18. 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 4th 5th First
5
weeks
Money
that
Lee
Earned
$240 $350 $460 … ? Sn

an=240+(n-1)110
a5=240+(5-1)110=680
We can use the formula:
Thus, =2300

19. 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 has
30 rows of seats

20. 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
30
th row. We can use this back in our formula
for the arithmetic series.