**Math Arithmetic Progressions**Advertisement

This unit introduces arithmetic sequence and series, Such that the difference between the consecutive term is constant,It also explores particular types of sequence known as arithmetic progressions (APs).

**Example** : 2, 4, 6, 8, 10.

Arithmetic Series : The sum of the numbers in a finite arithmetic progression is called as Arithmetic series.

**Example** : 2 + 4 + 6 + 8 + 10.

Its follows some pattern.

**Formula**: a_{n} = a + (n-1)d

s_{n} = (a_{1} + a_{n})n / 2

a_{1} = first term of the arithmetic progression

a_{2} = last term of the arithmetic progression

n = number of patterns

**Example** : What would be the 56th term in the series of 19, 22, 25, 28

**Answer** :

First term a = 19

Common difference d = 22-19 = 3.

Position of the term in the series n = 56

t_{n} = a + (n-1)d

t_{n} = 19 + (56-1)3

19+55*3 = 19+165 = 184.

So 56th term of the given series is 184.

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