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

Concept: Arithmetic Progression

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