CBSEi Class 10 Sequences (AP and GP) CORE

The fixed number is called the common difference of the progression and is
usually denoted by d.
Thus in (i), common difference (d) is 1, In (ii), common difference is 2 and in (iii),
common difference is 5.
The first term of an arithmetic progression (AP) is usually written as a.
Thus, in general,
If a is the first term and d, the common difference of an AP, then the AP can be
written as a, a + d, a + 2d, a+3d, ….
Note that in case of an AP, it is obvious that
common difference
= second term – first term
= third term – second term
= fourth term – third term and so on.
Example 4: Identify which of the following are arithmetic progressions. For those which
are arithmetic progressions, find the common differences :
(i) 3, 6, 12, 24,……
(ii) 12, 2, – 8, – 18,……
(iii) 0, , , , …….
(iv) , , , , .……
(v) 1, 1.7, 2.4, 3.1, …….
(vi) 1 2 , 5 2 , 7 2 , 73,…….
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