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SAI International School

Class X

Mathematics – Lesson Notes
Chapter-5: Arithmetic Progression

th
Sub topics: n term of A.P.

GENERAL FORM-

Let us denote the first term of an AP by a 1 , second term by a 2 , . . ., nth term by a n and
the common difference by d.

Then the AP becomes a 1 , a 2 , a 3 , . . ., a n .

So, a 2 – a 1 = a 3 – a 2 = . . . = a n – a n–1 = d

a, a + d, a + 2d, a + 3d, . . . represents an arithmetic progression where a is the first
term and d the common difference. This is called the general form of an AP.

For example-

a = – 7, d = – 2, the AP is – 7, – 9, – 11, – 13, . . .

a = 1.0, d = 0.1, the AP is 1.0, 1.1, 1.2, 1.3, . . .

a = 0, d = , the AP is 0, , 3, , 6, . . .

a = 2, d = 0, the AP is 2, 2, 2, 2, . . .

In an AP, every succeeding term is obtained by adding d to the preceding term. So, d
found by subtracting any term from its succeeding term, i.e., the term which immediately
follows it should be same for an AP.

For the list of numbers :

6, 3, 0, – 3, . . .,

a 2 – a 1 = 3 – 6 = – 3
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