The document defines and provides examples of number sequences, including arithmetic sequences. An arithmetic sequence starts with a number and each subsequent term is found by adding a common difference. The general form of an arithmetic sequence is Xn = an + b. The nth term is given by a + (n-1)d, where a is the first term and d is the common difference. Formulas are provided for calculating the sum of natural numbers, odd numbers, and the terms of an arithmetic progression.

2. ST. THOMAS
TRAINING COLLEGE.

4. NUMBER SEQUENCE
A collection of numbers
written in order as the first,
second, third and so on…

5. Number sequence from
real life
The petals of sunflower
Holes of a honey comb
Graiz on a maize cob
The length of a the rungs of
a ladder .

6. Examples…
1.
2
3. 100, 200, 300,…
4. 1,1,2,3,5,8,13,….

7. ARITHMETIC
SEQUENCE
A sequence which starts
with any number(a) and
proceed by addition of
one number (d) again
and again give arithmetic
sequence (arithmetic
progression)

8. Examples…
 1, 2, 3, 4, 5….
 ½ , 1 , 3/2 , 2 …
 1 ,4, 7,10, 13…
 In general a, a+d, a+2d
…..

9. Xn = an+b
is general
form of an A.P

10. nth term of an A.P
a+(n-1)d
Where a first term,
d common difference

11. Sum of natural
numbers
n(n+1)/2

12. Sum of odd
numbers


13. Sum of A.P
S= n/2[2a+(n-1)d]