Question

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

$-1.2,-3.2,-5.2,-7.2\dots$

Answer 1

Step 1. Find if the given series is in AP or not

Given series is $-1.2,-3.2,-5.2,-7.2\dots$

The common difference is,

$$\begin{gathered} (-3.2)-(-1.2)=-2 \\ (-5.2)-(-3.2)=-2 \\ (-7.2)-(-5.2)=-2 \end{gathered}$$

Since, the common difference is same every time.

Therefore, $d=-2$ and the given series are in A.P.

Step 2. Determine the next three term.

Thus, next three terms are:

$$\begin{gathered} –7.2-2=-9.2 \\ -9.2-2=–11.2 \\ -11.2-2=–13.2 \end{gathered}$$

Hence, the given series is an A.P and the next three terms are $-9.2,-11.2,-13.2$.