21. For the given A.P find the missing term →5,0,0, 19/4.
(a) 7/2, 9/2
(b) 15/2,8
(c) 13/2,8 (d) 15/4, 17/4
thon the ratio ofits com
onding
Answers
Answer:
(i) For this A.P.,
a=2
a
3
=26
We know that, a
n
=a+(n−1)d
a
3
=2+(3−1)d
26=2+2d
24=2d
d=12
a
2
=2+(2−1)12
=14
Therefore, 14 is the missing term.
(ii) For this A.P.,
a
2
=13 and
a
4
=3
We know that, a
n
=a+(n−1)d
a
2
=a+(2−1)d
13=a+d ... (i)
a
4
=a+(4−1)d
3=a+3d... (ii)
On subtracting (i) from (ii), we get,
−10=2d
d=−5
From equation (i), we get,
13=a+(−5)
a=18
a
3
=18+(3−1)(−5)
=18+2(−5)=18−10=8
Therefore, the missing terms are 18 and 8 respectively.
(iii) For this A.P.,
a
1
=5 and
a
4
=9
2
1
We know that, a
n
=a+(n−1)d
a
4
=5+(4−1)d
9
2
1
=5+3d
d=
2
3
a
2
=a+d
a
2
=5+
2
3
a
2
=
2
13
a
3
=a
2
+
2
3
a
3
=8
Therefore, the missing terms are 6
2
1
and 8 respectively.
(iv) For this A.P.,
a=−4 and
a
6
=6
We know that,
a
n
=a+(n−1)d
a
6
=a+(6−1)d
6=−4+5d
10=5d
d=2
a
2
=a+d=−4+2=−2
a
3
=a+2d=−4+2(2)=0
a
4
=a+3d=−4+3(2)=2
a
5
=a+4d=−4+4(2)=4
Therefore, the missing terms are −2,0,2, and 4 respectively.
(v) For this A.P.,
a
2
=38
a
6
=−22
We know that
a
n
=a+(n−1)d
a
2
=a+(2−1)d
38=a+d... (i)
a
6
=a+(6−1)d
−22=a+5d ... (ii)
On subtracting equation (i) from (ii), we get
−22−38=4d
−60=4d
d=−15
a=a
2
−a=38−(−15)=53
a
3
=a+2d=53+2(−15)=23
a
4
=a+3d=53+3(−15)=8
a
5
=a+4d=53+4(−15)=−7
Therefore, the missing terms are 53,23,8 and −7 respectively.