The document explains different types of sequences, focusing on arithmetic sequences, and provides formulas to find the general nth term. It also includes examples and exercises demonstrating how to calculate various terms in an arithmetic sequence, as well as word problems that apply these concepts. The document illustrates practical scenarios where arithmetic sequences are utilized, such as training schedules.

1. KINDS OF SEQUENCE
ARITHMETIC SEQUENCE
A
B
C
D
GEOMETRIC SEQUENCE
HARMONIC SEQUENCE
FIBONACCI SEQUENCE

2. 2, 4, 6, 8, 10, …
ü Is a sequence of numbers such
that the difference of any two
consecutive terms is the same.
2 2 2 2
Common Difference

3. Where:
ü tn = Last Term
ü t1 = First Term
ü n = Number of Terms
ü d = Common Difference
ARITHMETIC SEQUENCE FORMULA
tn = t1 + (n – 1)d

4. Finding the General nth term of Arithmetic Sequence
3, 7, 11, 15, 19, …
ütn = ?
üt1 = 3
ün = ?
üd = 4
tn = 3 + (n – 1) 4
tn = 3 + 4n – 4
tn = 3 – 4 + 4n
tn = 4n - 1
General nth term
tn = t1 + (n – 1)d
Checking:
Find first Term: 3
tn = 4n - 1
t1 = 4(1) - 1
t1 = 4 – 1
t1 =
3

5. Find the general nth term of the arithmetic sequence with
common difference of and whose first term is .
3 12
ütn = ?
üt1 = 12
ün = ?
üd = 3
tn = 12 + (n – 1) 3
tn = 12 + 3n – 3
tn = 12 – 3 + 3n
tn = 3n + 9
General nth term
Checking:
Find first Term: 12
tn = 3n + 9
t1 = 3(1) + 9
t1 = 3 + 9
t1 =

6. Finding the General nth term of Arithmetic Sequence
ütn = ?
üt1 = -8
ün = ?
üd = 6
tn = -8 + (n – 1) 6
tn = -8 + 6n – 6
tn = -8 – 6 + 6n
tn = 6n - 14
Checking:
Find Third Term(n = 3): 4
tn = 6n - 14
t3 = 6(3) – 14
t3 = 18 – 14
t3 = 4

7. 26, 30, 34, 38, 42
ü t1 = 6
ü d = 4
ü n = 10
ü t10 = ?
t10 = 6 + (10 – 1) 4
t10 = 6 + (9) 4
t10 = 6 + 36
t10 = 42

8. Find the 52nd term of the sequence
ü t1 = 7
ü d = 6
ü n = 52
ü t52 = ?
t52 = 7 + (52 – 1) 6
t52 = 7 + (51) 6
t52 = 7 + 306
t52 = 313

9. ü t1 = -12
ü d = 5
ü n = 37
ü t37 = ?
t37 = -12 + (37 – 1) 5
t37 = -12 + (36) 5
t37 = -12 + 180
t37 = 168

10. Find the 46th term of the sequence
ü t1 = 38
ü d = -9
ü n = 46
ü t46 = ?
t46 = 38 + (46 – 1) -9
t46 = 38 + (45) -9
t46 = 38 - 405
t46 = - 367

11. WORD PROBLEMS INVOLVING
ARITHMETIC SEQUENCE

12. Josh decides to compete in a marathon and
begins to train for it. On the first day, he visits
the gym and trains for 1 hour. If he increases his
training time by 30 mins each day, how long will
he train for at the end of the week?

13. First term is 60
Common difference is 30
number of terms is 7
ü t1 = 60
ü d = 30
ü n = 7
ü t7 = ?
t7 = 60 + (7 – 1) 30
t7 = 60 + (6)30
t7 = 60 + 180
t7 = 240
t7 = 4hours
He will train for
240 mins or 4
hrs at the end
of the week

14. After a knee surgery, your trainer tells you to
return to your jogging for 12 mins each for the
first week. Each week thereafter, he suggests
you increase that time by 6 mins. How many
weeks will it be before you are up to jogging 60
mins per day?

15. First term is 12
Common difference is 6
Last term is 60
ü t1 = 12
ü d = 6
ü n = ?
ü tn = 60
60 = 12 + (n – 1) 6
60 = 12 + 6n - 6
60 = 12 - 6 + 6n
60 = 6 + 6n
60 – 6 = 6n
54 = 6n
9 = n
It will take 9
weeks to be
running 60
mins per day