Question

Prove:

If each term of an A.P. is divided by a non-zero constant then the resulting sequence is also an A.P.

Answer 1

Let the series is

$a,a+d,a+2d,a+3d.......$

now dividing it by a non zero number $n$

so $\frac{a}{n},\frac{a}{n}+\frac{d}{n},\frac{a}{n}+\frac{2d}{n},\frac{a}{n}+\frac{3d}{n}$

So as you can see the common difference charged from $d$ to $d/n$ but stull is is in $A.P.$