(i) For this A.P.,
a=2
a3=26
We know that, an=a+(n−1)d
a3=2+(3−1)d
26=2+2d
24=2d
d=12
a2=2+(2−1)12
=14
Therefore, 14 is the missing term.
(ii) For this A.P.,
a2=13 and
a4=3
We know that, an=a+(n−1)d
a2=a+(2−1)d
13=a+d ... (i)
a4=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
a3=18+(3−1)(−5)
=18+2(−5)=18−10=8
Therefore, the missing terms are 18 and 8 respectively.
(iii) For this A.P.,
a1=5 and
a4=912
We know that, an=a+(n−1)d
a4=5+(4−1)d
912=5+3d
d=32
a2=a+d
a2=5+32
a2=132
a3=a2+32
a3=8
Therefore, the missing terms are 612 and 8 respectively.
(iv) For this A.P.,
a=−4 and
a6=6
We know that,
an=a+(n−1)d
a6=a+(6−1)d
6=−4+5d
10=5d
d=2
a2=a+d=−4+2=−2
a3=a+2d=−4+2(2)=0
a4=a+3d=−4+3(2)=2
a5=a+4d=−4+4(2)=4
Therefore, the missing terms are −2,0,2, and 4 respectively.
(v) For this A.P.,
a2=38
a6=−22
We know that
an=a+(n−1)d
a2=a+(2−1)d
38=a+d... (i)
a6=a+(6−1)d
−22=a+5d ... (ii)
On subtracting equation (i) from (ii), we get
−22−38=4d
−60=4d
d=−15
a=a2−a=38−(−15)=53
a3=a+2d=53+2(−15)=23
a4=a+3d=53+3(−15)=8
a5=a+4d=53+4(−15)=−7
Therefore, the missing terms are 53,23,8 and −7 respectively.