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