A sequence is an ordered list of items, typically numbers, which can be finite or infinite. There are different types of sequences, such as arithmetic sequences with a constant difference, geometric sequences where each term is multiplied by a constant, and special sequences like triangular, square, and Fibonacci numbers, each following specific rules to determine their terms. Understanding these sequences involves recognizing the patterns and formulas that generate their terms.

1. Sequence

2. What is a Sequence?
> A Sequence is a list of things (usually numbers) that
are in order.

3. Infinite or Finite
When the sequence goes on forever it is called an
infinite sequence,
otherwise it is a finite sequence
1. {1, 2, 3, 4, ...}
2. {1, 3, 5, 7}
3. {a, b, c, d, e}
4. {a, n, n, a, b}

4. A Rule
A Sequence usually has a Rule, which is a way to find the
value of each term.

5. Arithmetic Sequences
In an Arithmetic Sequence the difference between one term and the
next is a constant.
Example:
1, 4, 7, 10, 13, 16, 19, 22, 25, ...
Rule: xn = 3n-2
arithmetic sequence like this: {a, a+d, a+2d, a+3d, ... }
the rule: xn = a + d(n-1)

6. Geometric Sequences
In a Geometric Sequence each term is found by
multiplying the previous term by a constant.
Example: 2, 4, 8, 16, 32, 64, 128, 256, ...
Its Rule is xn = 2n
Geometric sequence like this: {a, ar, ar2, ar3, ... }
 the rule is: xn = ar(n-1)

7. Triangular Numbers
The Triangular Number Sequence is generated from a
pattern of dots which form a triangle.
Ex- 1, 3, 6, 10, 15, 21, 28, 36, 45, ...
Rule:- xn = n(n+1)/2

8.  Square Numbers
1, 4, 9, 16, 25, 36, 49, 64, 81, ... xn = n2
 Cube Numbers
1, 8, 27, 64, 125, 216, 343, 512, 729, ... xn = n3
 Fibonacci Sequence
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... xn = xn-1 + xn-2

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