Difference between Arithmetic Series and Geometric series and also differentiate between Arithmetic Sequence and Geometric sequence

2. PREPARED BY:
MUHAMMAD ZARYAB

3. SEQUENCE
 Arithmetic sequence / Arithmetic progression
 Geometric sequence / Geometric progression
SUMMATION
Sigma notation

8. SEQUENCE:
A sequence is just a list of elements usually written in a row.
EXAMPLES:
1. 1, 2, 3, 4, 5, …
2. 4, 8, 12, 16, 20,…
3. 2, 4, 8, 16, 32, …
4. 1, 1/2, 1/3, 1/4, 1/5, …
5. 1, -1, 1, -1, 1, -1, …
Find the first 4 terms
C n = 1+ (-1) ^n for all integers n ≥ 0
a n = (-1) n for all integers n ≥ 0
bj = 1 + 2j, for all integers j ≥ 0
An=n+1/2n+5 for all integers n ≥ 0

9. Find the explicit formula
1. 1-1/2 , 1/2-1/3 , 1/3-1/4
2. 2, 6, 12, 20, 30, 42, 56, …
3. 1/4, 2/9, 3/16, 4/25, 5/36, 6/49, …
Find the specified term of A.P
1)3,7,11......61 term
2)6,4,2....45 term
3)-4,-7,-10,.....19 term

10. Find the term indicated in following sequence
1) 2,6,11,17....a8
2) 2)1,1/3,1/9,1/27...a5
Find the missing element of A.P
a=2,an=402 ,n=26
A=16, an=0 ,d=-1/4
Find the 15th term of A.P where 3rd term is 8 and
common difference is 1/8;
Which term of A.P is 6,2,-2,..........is -146
Find the nth term of A.P where An-5=3n+9
Find the nth term of A.P (3/4)2 , (3/7)2 , (3/10)2

11. Find A.M between X2 +X+1 , X2 -X+1 ;
If 3 and 6 are two A.Ms between a and b ,find A and B;
Find 6 A.Ms between 7 and 13;
If the A.M 9 and B is 27 ,find the valve of B;

12. GEOMETRIC SEQUENCE:
A sequence in which every term after the first is
obtained from the preceding term by multiplying it
with a constant number is called a geometric sequence
or geometric progression (G.P.)
the common ratio of the G.P. commonly denoted by “r”.
EXAMPLE:
1. 1, 2, 4, 8, 16, … (common ratio = 2)
2. 3, - 3/2, 3/4, - 3/8, … (common ratio = - 1/2)
3. 0.1, 0.01, 0.001, 0.0001, … (common ratio = 0.1 = 1/10)

15. Find the 8th term of the following geometric sequence 4, 12, 36, 108, …
Which term of the geometric sequence is 1/8 if the first term is 4 and
common ratio ½
Write the geometric sequence with positive terms whose second term is 9
and fourth term is 1
Write the geometric sequence with positive terms whose second term is 9
and fourth term is 1.
Find the missing term
R=10,an=100,a=1;
A=128 ,r=1/2 ,an=1/4
If the three A.Ms between A and B are 5,9,13 Find A and
B.

18. SUMMATION NOTATION:
The capital Greek letter sigma ∑ is used to write a sum in
a short hand notation. where k varies from 1 to n
represents the sum given in expanded form by = a1 +
a2 + a3 + … + an

19. How important the subject
discrete structure in computer
programming ?
 Used to arrange Apps(Application) in any sequence
 Used to arrange your Phone contacts in any sequence
 Discrete Structure gives you complete structure about
computer programming
 Without discrete structure you don’t gave any sequence
in your programming.
 Ask examples , like arranging array, char array

20. THANK YOU