Question

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

$a,2a,3a,4a\dots$

Answer 1

Arithmetic Progression:

The given series is $a,2a,3a,4a\dots$

The difference between each term is;

$$\begin{gathered} 2a–a=a \\ 3a-2a=a \\ 4a-3a=a \end{gathered}$$

Since, the common difference is same every time.

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

So, the next three terms are;

$$\begin{gathered} 4a+a=5a \\ 5a+a=6a \\ 6a+a=7a \end{gathered}$$

Hence, the given series is an A.P. and the common difference is $d=a$and the next three terms are $5a,6a,7a$.