Question

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

$-10,-6,-2,2\dots$

Answer 1

Arithmetic Progression:

The given series is $-10,-6,-2,2\dots$

The difference between each term of the given series is:

$$\begin{gathered} (-6)-(-10)=4 \\ (-2)-(-6)=4 \\ \left(2\right)-(-2)=4 \end{gathered}$$

Since, the common difference is same every time.

Therefore, $d=4$ and the given numbers are in A.P.

So, the next three terms are:

$$\begin{gathered} 2+4=6 \\ 6+4=10 \\ 10+4=14 \end{gathered}$$

Hence, the given series is an A.P. and common difference is $d=4$ and the next three terms are $6,10,14$.