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ARITHMETIC

PROGRESSIONS

  • Introduction of ‘an’ formula

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a1

First term

a2

Second term

a3

Third term

an

nth term /Any term / General term

where ‘n’ is the term position / term number

E.g. – For 25th Term, n = 25

For 28th Term, n = 28

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For a given AP:

We know that,

a2 =

a1 + d

a3 =

a4 =

a5 =

a2 + d

a3 + d

a4 + d

a1 =

a

a + d

a + d + d

a + 2d

a + 2d + d

a + 3d

a + 3d + d

a + 4d

Replace ‘a1’ by ‘a’

Replace ‘a2’ by ‘a + d’

Replace ‘a3’ by ‘a + 2d’

Replace ‘a4’ by ‘a + 3d’

a + (5 – 1) d

a + (4 – 1) d

a + (3 – 1) d

a + (2 – 1) d

a + (1 – 1) d

∴ an =

a + (n – 1) d

=

=

=

=

=

is the nth term of an AP

4

3

2

1

+ 0d

Replace 4 by

(5 – 1)

Replace 3 by

(4 – 1)

Replace 2 by

(3 – 1)

Replace 1 by

(2 – 1)

Replace 0 by

(1 – 1)