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

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by dimplerckzz

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by dimplerckzz

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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.