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# 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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