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Sequence

A sequence is a collection of numbers and terms.Sequence may be finite and infinite.

Finite sequence :

$$\{a_1,a_2,a_3,a_4,a_5\}$$

Infinite sequence :

$$\{a_1,a_2,a_3,a_4,......a_n\}$$

Arithmetic sequence

A pattern of terms or numbers that increase or decrease at a constant amount.

Example:

$$\{1,5,9,13,17,21,25,29,33\}$$

This sequence has a difference of 4 between each number.

We could write like that:

$$\{a,a+d,a+2d,a+3d,......\}$$

a is the first term, and

d is the difference between them.

Now

$$a = 1$$

$$d = 4$$

So,

{1,1+4,1+2*4,1+3*4,1+4*4,1+5*4,...}

$$\{1,5,9,13,17,21……….\}$$