Question

What do you observe when you multiply or divide a fixed number with each and every term of arithmetic progression

Answer 1

The numbers would still be in arithmetic progression, though the common difference would be changed.
Let the numbers of the arithmetic sequence be a, b, c ..
Common difference = b-a
When x is multiplied to all the terms, the arithmetic progresion becomes
xa, xb, xc ..
Common difference = xb - xa = x(b-a)
Thus the common difference increases by a factor of x.
When y is divided from all the terms, the arithmetic progression becomes
a/y, b/y, c/y ...
Common difference = b/y - a/y = (b-a)/y
Thus the common difference decreases by a factor of y.