Question 4 (vii)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(vii) 0, - 4, - 8, - 12 …

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Solution

(vii) $0, - 4, - 8, - 12 \dots \dots$
Here,
$a_{2} - a_{1} = (- 4) - 0 = - 4 a_{3} - a_{2} = (- 8) - (- 4) = - 4 a_{4} - a_{3} = (- 12) - (- 8) = - 4$
$\Rightarrow a_{n + 1} - a_{n}$ is same everytime.
Therefore,d=-4 and the given numbers are in A.P.
Next three terms are:
$a_{5} = - 12 - 4 = - 16 a_{6} = - 16 - 4 = - 20 a_{7} = - 20 - 4 = - 24$

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