Question

insert two arithmetic mean between -2and 7​

Answer 1

Question:

Insert two arithmetic mean between - 2 and 7 .

Answer:

1 , 4

Note:

• If some arithmetic means are inserted between two numbers , then the sequence as a whole forms an Arithmetic Progression.

• If n arithmetic means are inserted between a and b , then ; a , A1 , A2 , A3 , ... , An , b forms an Arithmetic Progression ,

where A1 , A2 , A3 ....... An are the n arithmetic means to be inserted between a and b .

• The common difference of the obtained A.P. after inserting n arithmetic means between a and b is given as ; d = (b - a)/(n + 1) .

[ For proof , please refer to the attachment ]

• And hence , the n arithmetic means will be ;

A1 = a + d

A2 = a + 2d

A3 = a + 3d

:

:

An = a + nd

Solution:

Here,

We need to insert two arithmetic means between -2 and 7 .

Thus,

a = -2

b = 7

n = 2

Now ,

Let the arithmetic means to be inserted be A1 and A2 .

Thus,

The obtained A.P. will be as ;

-2 , A1 , A2 , 7

Also,

The common difference of the obtained A.P. will be given as ;

=> d = (b - a)/(n + 1)

=> d = { 7 - ( - 2 ) } / ( 2 + 1 )

=> d = (7 + 2)/(2 + 1)

=> d = 9/3

=> d = 3

Now,

The required arithmetic means will be given as ;

A1 = a + d = -2 + 3 = 1

and

A2 = a + 2d = -2 + 2•3 = -2 + 6 = 4

Hence,

The required arithmetic means are 1 and 4 .