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. A_{1} and A_{2} are two arithmetic mean between two member a and ‘b’ then a, A_{1}, A_{2} b are in A.P.

Now using the formula,

t_{n} = a+(n–1)d

or, d = b–a/3 [ here n = 4]

so, A_{1} = a + d = a +b–a/3 = 2a+b/3

and A_{2} = a + 2d = a + 2(b–a)/3 = a+2b/3

**To read more, Buy study materials of ****Sequences and Series**** comprising study notes, revision notes, video lectures, previous year solved questions etc. Also browse for more study materials on Mathematics ****here**.

Complete Your Profile

Get your questions answered by the expert for free

Enter text here...