Math1

Sequences

Sequences are a ordered group of numbers. They are represented as < variable-name >

Example:

<a> = 1, 4, 7, 10

Some pointers :-

Sequences may or may not be governed by a rule. Such sequences that are not governed by any rule are not of our interest, neither of any Higher studies in Mathematics.

Example:

<n> = 1, 2, 17, 10, 21, 15

Now, what interests us is sequence of numbers that are defuned by a rule. This is because as we get the fixed rule, we could generate the sequences as long as we desire.

Example:

<m> = 2, 4, 6, 8, 10, ...  

  (governed by rule $a_n$ = 2n)

Such sequences are of our importances as they can be extended to infinite terms. We call such rule governed sequences as Progressions. Let is lead into Progressions (it is just a subset of Sequences, not a separate heading to be honest).

~ Progression

E1

$\sum\limits^{n}_{k=1} a_k$