In the following APs find the missing term in the boxes.
In the following APs find the missing term in the boxes.

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 = + 2= 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.