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1. National College of Business Administration & Economics

2. Group Members
-40
Muhammad Ahsan
Shahid Zafar
Sarmad Shuja
Wamiq Ali
Zain Abid
01
02
03
04
05

3. INSERT THE TITLE
OF YOUR PRESENTATION HERE
DS
PPT

4. The sequence and series have important applications in Physics, Geography, Biology, Economics,
Psychology, Engineering, Chemistry, Computer science and Finance.
Introduction

5. Sequence
A sequence is an arrangement of any objects or a set of numbers in a particular
order followed by some rule. If a1, a2, a3, a4, ……… etc. Denote the terms of a
sequence, then 1,2,3,4, …

6. 𝟐𝟓, 𝟐𝟏, 𝟏𝟕, 𝟏𝟑, 𝟗, … .
Example:

7. Sequence in Computer Science
In Programming, sequence is the basic algorithm: A set of logical steps carried
out in order that commands are executed by a computer, allows us to carry out
tasks that have multiple steps.
Microprocessor also follow a sequence which is Fetch, Decode, and then Execute.

8. Necessary Tools For Microprocessor
Arithmetic Progression
AP
01
Arithmetic Mean
AM
02
Geometric Progression
GP
03
Harmonic Progression05
Geometric Mean
GM
04
Harmonic Mean06
HP
HM

9. Arithmetic Progression
An Arithmetic Progression is a sequence in which every term is obtained by
adding some fix number to the preceding term. The fix number to preceding term.
The fix number is the common difference of two consecutive terms denoted by d.

10. Find the 10th term if 𝑎3 = 8 and 𝑎7 = 16
Example:

11. Arithmetic Mean
Let a and b be two numbers, than a number A is set to be A.M between a and b if
a, A, b are in A.P
Thus A - a = b – A
2A =a +b
A = a+b/2

12. Find A.M between
2𝑥 + 1, 4𝑥 + 3
Example:

13. Geometric Progression
A sequence in which every term is obtained by multiplying or dividing a definite nu
mber with the preceding number is known as a geometric sequence.
𝑟 =
𝑎 𝑛
𝑎 𝑛−1
𝑛 > 1 , ∀𝑛 ∈ 𝑁, 𝑎 𝑛−1 ≠ 0

14. Find 𝑎 𝑛 if 𝑎4 =
8
27
and 𝑎7 −
64
729
of a G.P.
Example:

15. Geometric Mean
Let a and b two numbers. A number G is said to be geometric mean between two
numbers a and b if a, G, b are in G.P,so
𝐺
𝑎
=
𝑏
𝐺
𝐺2
= 𝑎𝑏
𝐺 = ±𝑎𝑏

16. Find G.M between
2i and -4i
Example:

17. Harmonic Progression
If the reciprocal of the terms of the sequence form an A.P, then sequence is called
harmonic.

18. Find the 8th term of H.P:
1
2
,
1
5
,
1
8
, …
Example:

19. Harmonic Mean
Let a and b be two numbers, then a number H is called Harmonic mean between t
wo numbers a and b if a,H,b are in H.P

20. Example:

21. Uses of Sequence
 A sequence is a discrete structure used to represent an ordered list.
 A sequence is a function from a subset of the set of integers (usually
either the set {0,1,2.. ..} Or {1,2, 3,...}To a set S.
 We use the notation an to denote the image of the integer n.....
 Notation to represent sequence is {an}

22. Advantages:
The common 2-year sequence works well for many disciplines. Topics can be
introduced "just-in-time" for many disciplines. Since all students take the same
sequence, advising is relatively easy.

23. Thank You 