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Which of the following are APs? If they form an A.P. find the common difference d and write three more terms:

-10, - 6, - 2, 2 …

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#### Solution

−10, −6, −2, 2 …

It can be observed that

a_{2} − a_{1} = (−6) − (−10) = 4

a_{3} − a_{2 }= (−2) − (−6) = 4

a_{4} − a_{3} = (2) − (−2) = 4

i.e., a_{k}_{+1 }− a_{k} is same every time. Therefore, d = 4

The given numbers are in A.P.

Three more terms are

a_{5} = 2 + 4 = 6

a_{6} = 6 + 4 = 10

a_{7} = 10 + 4 = 14

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