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# Math Arithmetic Progressions

## Math Arithmetic Progressions

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: an = a + (n-1)d

sn = (a1 + an)n / 2
a1 = first term of the arithmetic progression
a2 = 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
tn = a + (n-1)d
tn = 19 + (56-1)3
19+55*3 = 19+165 = 184.
So 56th term of the given series is 184.

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