Question

Which of the following are APs?

If they form an A.P. find the common difference d and write three more terms.

$0,-4,-8,-12\dots$

Answer 1

Step 1.Determine if the given term are in AP are not.

The given series is

$0,-4,-8,-12\dots$

The common difference is

$$\begin{gathered} (-4)-0=-4 \\ (-8)-(-4)=-4 \\ (-12)-(-8)=-4 \end{gathered}$$

Since, the common difference is same every time.

Therefore, $d=-4$ and the given series forms a A.P.

Step 2. Find the next three term.

Hence, the next three terms are:

$$\begin{gathered} -12-4=-16 \\ -16-4=-20 \\ -20-4=-24 \end{gathered}$$

Hence, the given series is an A.P. and the common difference is $d=-4$ and the next three terms are $-16,-20,-24$.