Solution:
(i) In the case of given A.P.,
a2 = 38
a6 = −22
As we all know, for an A.P.,
an = a+(n −1)d
Therefore, putting the values here,
a2 = a+(2−1)d
38 = a+d ……………………. (i)
a6 = a+(6−1)d
−22 = a+5d …………………. (ii)
On subtracting the equation (i) from equation (ii), we get
− 22 − 38 = 4d
−60 = 4d
d = −15
a = a2 − d = 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.