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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.0, - 4, - 8, - 12,

We have,

a2 – a1 = -4 – 0 = -4

a3 – a2 =-8 – (-4) = -8 + 4 = -4

a4 – a3 =-12 – (-8) = -12 + 8= -4

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

So, the given list of numbers forms an AP with the common difference d = -4

Now, we have to find the next three terms.

We have a1 = 0, a2 = -4, a3 = -8 and a4 = -12

Now, we will find a5, a6 and a7

So, a5 = -12 + (-4) = -12 – 4 = -16

a6 = -16 + (-4) = -16 – 4 = -20

and a7 = -20 + (-4) = -20 – 4 = -24

Hence, the next three terms are -16, -20 and -24

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