# EXERCISE 19.6

**QUESTION 1**

Find the A.M. between:

(i) 7 and 13

Sol :

Let be the A.M. between 7 and 13

= 10

(ii) 12 and -8

Sol :

Let be the A.M. between 12 and -8

= 2

(iii) (x – y) and (x + y)

Sol :

Let be the A.M. between and

= *x*

**QUESTION 2**

Insert 4 A.M.s between 4 and 19

Sol :

Let ,,, be the four A.M.s between 4 and 19 Then, 4, ,,, and 19 are in A.P. whose common difference is as follows:

a = 4 ,

n = 6

d = 3

Hence, the required A.M.s are , 7 , 10 , 13 , 16

**QUESTION 3**

Insert 7 A.M.s between 2 and 17

Sol :

Let ,,,,,, be the seven A.M.s between 2 and 17

Then, ,,,,, ,, and 17 are in A.P. whose common difference is as

follows:

Here , we have

a = 2 ,

n = 9

Hence, the required A.M.s are ,, , ,,,,

**QUESTION 4**

Insert six A.M.s between 15 and -13.

Sol :

Let , ,,,, be the 6 A.M.s between 15 and -13

Then, 15,,,, , , and -13 are in A.P. whose common difference is as follows:

We have :

a = 15 ,

n = 8

d = -4

Hence, the required A.M.s are 11 , 7 , 3 , -1 , -5 , -9

**QUESTION 5**

There are *n* A.M.s between 3 and 17 . The ratio of the last mean to the first mean is Find the value of *n*

Sol :

Let , ,,, be the n A.M.s between 3 and 17

Let *d *be the common difference of the A.P 3 , , ,,, and 17 . Then we have

a = 3 ,

total terms = n

Now ,

**QUESTION 6**

Insert A.M.s between 7 and 71 in such a way that the A.M. is 27 Find the number of A.M.s.

Sol :

Let , ,,, 27 ,, be the *n* A.M.s between 7 and 71