1. Solve the problem progression and series
Concept Map
􀂊Pattern number, progression, and series
􀂊Sigma Notation
􀂊Progression and series arithmetic
􀂊nth term arithmetic progression
􀂊Arithmetic series
􀂊Progression and series geometric
􀂊nth term geometric progression
􀂊Geometric series
􀂊Infinite geometric series
Applying the concept of progression and series in the problem-solving
Solve the problem progression and series

2. Pattern number, progression, and series
Pattern number is rules in determining the number of one to the next number on each progression is.
Progression is organized in a sequential pattern based on the number.
Series is the number of all numbers that are on progression.
Example :
1. 1, 3, 5, 7, 9, ….  odd number
2. 2, 4, 6, 8, 10, ….  even number
3. 2, 6, 12, 20, 30, ….  rectangular number
4. 1, 3, 6, 10, 15, ….  triangular number
5. 1, 4, 9, 16, 25, ….  square number

3. Example : Be discovered progression : 2, 5, 10, 17, … Find :
a. term to-n formula :
U1 = 2 = =
U2 = 5 = =
U3 = 10 = =
U4 = 17 = =
Un = … = … + 1= n2 + 1
so term to-n formula is Un = n2 + 1
b. Numbers on term to-20 (U20) :
U20 = = 401
c. term to which the size of the 170
(Un = 170)
Un = 170 = n2 + 1
n2 = 169
n = 13

4. Sigma Notation is a way to write a short summation.
Rule sigma notation
Eg ak and bk is term to-k and C constant .
1. If ak = C, then 2. 3. 4. 5.

5. Example : 1. Indicate series 1 + 4 + 7 + … + 22 with sigma notation :
3.n – 2 = 22  n = 8 2.

6. Progression and series Arithmetic
Arithmetic progression is progression where the difference between the two tribes that sequence is always the same value.
Un = a + (n – 1).b
where ;
Un = The n-th term
a = first term
b = difference, with b = Un – Un -1
n = order, with n = 1, 2, 3, …

7. Progression and series Arithmetic
Arithmetic series the sum of the members of a finite arithmetic progression. or
where ;
Sn = series arithmetic
Un = The n-th term
a = first term
b = difference, with b = Un – Un -1
n = order, with n = 1, 2, 3, …

8. Progression and series Geometric
A geometric progression is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio.
Un = a.rn-1
where ;
Un = The n-th term
a = first term
r = ratio, with
n = order, with n = 1, 2, 3, …

9. Progression and series Geometric
A geometric series is the sum of the numbers in a geometric progression.
for r ≠ 1 and r > 1, to be used
where ;
Sn = series geometric
Un = The n-th term
a = first term
r = ratio, with
n = order, with n = 1, 2, 3, …

10. Progression and series Geometric
Infinite series
For r ≠ 1 and – 1 < r < 1, to be used infinite series to convergence.
where ;
S = infinite series
a = first term
r = ratio, with