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Arithmetic mean between two numbers

When three numbers are in A.P., the middle term is called arithmetic mean (AM) of the two others.

Let a and b are two numbers.

And A be the arithmetic mean between two numbers.

So a A b are in A.P.

or,    A – a = b – A

or,    2A = a + b

        A =a+b/2

So, in general

A.M. = Sum of the numbers/2                                                     …… (5)

Similarly we can find the two arithmetic means between two number. A1 and A2 are two arithmetic mean between two member a and ‘b’ then a, A1, A2 b are in A.P.

Now using the formula,

        tn = a+(n–1)d

or,    d = b–a/3 [ here n = 4]

so,    A1 = a + d = a +b–a/3 = 2a+b/3

and   A2 = a + 2d = a + 2(b–a)/3 = a+2b/3

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