Q6 of 176 Page 9

Which of the following list of numbers form A.R's? If they form an A.P., find the common difference d and also write its next three terms.

a, 2a, 3a, 4a, ...

We have,


a2 – a1 = 2a – a = a


a3 – a2 = 3a – 2a = a


a4 – a3 = 4a – 3a = a


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


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


Now, we have to find the next three terms.


We have a1 = a, a2 = 2a, a3 = 3a and a4 = 4a


Now, we will find a5, a6 and a7


So, a5 = 4a + a = 5a


a6 = 5a + a = 6a


and a7 = 6a + a = 7a


Hence, the next three terms are 5a, 6a and 7a


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