Let us consider some examples
Example-1.For the AP : 1/4,-1/4,-3/4,-5/4 ........, write the first term a and the common difference d. And find the 7th term
Solution:Here, a = 1/ 4; d = -1/4 - 1/4 = -1/2
Remember that we can find d using any two consecutive terms, once we know that the numbers are in AP.
The seventh term would be -5/4 - 1/2 - 1/2 - 1/2 = -11/4
Example-2.Which of the following forms an AP? If they form an AP, then 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, . . . (v) x, 2x, 3x, 4x ......
Solution:(i) We have a2 – a1 = 10 – 4 = 6
a3 – a2 = 16 – 10 = 6
a4 – a3 = 22 – 16 = 6
i.e., ak + 1 – ak is 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) a2 – a1 = – 1 – 1 = – 2
a3 – a2 = – 3 – ( –1 ) = – 3 + 1 = – 2
a4 – a3 = – 5 – ( –3 ) = – 5 + 3 = – 2
i.e., ak + 1 – ak is 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