Question

Which of the following are APs?

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

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

Answer 1

Find if the given series is in AP or not.

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

The common difference is

$$\begin{gathered} a^2–a=a(a-1) \\ {a}^3–a^2=a^2(a-1) \\ {a}^4–a^3=a^3(a-1) \end{gathered}$$

Since, the common difference is not same every time.

Hence, the given series doesn’t forms an A.P.