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# How do we work out the nth term?

Arithmetic Progressions – An arithmetic progression is a series in which each term is derived by addition or subtraction of a common numeral to its previous term. The Arithmetic sequence formula is used for determining the nth term of an arithmetic progression.

The nth term formula is as below.

a= a1 + (n – 1) d

an = nth term to be calculated. a1 = the 1st term of the series.

n = number of terms. d = common difference

EXAMPLE

Find the 30th term of the arithmetic progression 0, 2, 4, 6, 8, 10, 12, 14, ……

The series = 0, 2, 4, 6, 8, 10, 12, 14, ……

By applying the nth term formula

a= a1 + (n – 1) d

a1 = 0 n = 30 d = 2

a30 = 0 + (30 – 1) 2

a30 = 29 × 2

a30 = 58

So, the 30th term of the sequence is 58.

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