NCERT Class 10 Mathematics

98 MATHEMATICS

Note that to find d in the AP : 6, 3, 0, – 3,.. ., we have subtracted 6 from 3
and not 3 from 6, i.e., we should subtract the kth term from the (k + 1) th term
even if the (k + 1) th term is smaller.

Let us make the concept more clear through some examples.

Example 1 : For the AP :^3
2

,^1

2

, –^1

2

, –^3

2

,.. ., write the first term a and the

common difference d.

Solution : Here, a =

3

2

, d =

1

2

–

3

2

= – 1.

Remember that we can find d using any two consecutive terms, once we know that
the numbers are in AP.

Example 2 : Which of the following list of numbers does form an AP? If they form an
AP, write the next two terms :

(i) 4, 10, 16, 22,... (ii) 1, – 1, – 3, – 5,...

(iii) – 2, 2, – 2, 2, – 2,... (iv) 1, 1, 1, 2, 2, 2, 3, 3, 3,...

Solution : (i) We have a 2 – a 1 = 10 – 4 = 6

a 3 – a 2 = 16 – 10 = 6

a 4 – a 3 = 22 – 16 = 6

i.e., ak + 1 – ak is the same every time.

So, the given list of numbers forms an AP with the common difference d = 6.

The next two terms are: 22 + 6 = 28 and 28 + 6 = 34.

(ii) a 2 – a 1 = – 1 – 1 = – 2

a 3 – a 2 = – 3 – ( –1 ) = – 3 + 1 = – 2

a 4 – a 3 = – 5 – ( –3 ) = – 5 + 3 = – 2

i.e., ak + 1 – ak is the same every time.

So, the given list of numbers forms an AP with the common difference d = – 2.

The next two terms are:

• 5 + (– 2 ) = – 7 and – 7 + (– 2 ) = – 9
  (iii)a 2 – a 1 = 2 – (– 2) = 2 + 2 = 4
  a 3 – a 2 = – 2 – 2 = – 4

As a 2 – a 1 a 3 – a 2 , the given list of numbers does not form an AP.