(i) For the given A.P., 2,2 , 26

The first and third term are;

a = 2

a₃ = 26

As we know, for an A.P.,

a_n = a+(n −1)d

Therefore, putting the values here,

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 the given A.P., , 13, ,3

a₂ = 13 and

a₄ = 3

As we know, for an A.P.,

a_n = a+(n−1) d

Therefore, putting the values here,

a₂ = a +(2-1)d

13 = a+d ………………. (i)

a₄ = a+(4-1)d

3 = a+3d ………….. (ii)

On subtracting equation (i) from (ii), we get,

– 10 = 2d

d = – 5

From equation (i), putting the value of d,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 the given A.P.,

a = 5 and

a₄ = 19/2

As we know, for an A.P.,

a_n = a+(n−1)d

Therefore, putting the values here,

a₄ = a+(4-1)d

19/2 = 5+3d

(19/2) – 5 = 3d

3d = 9/2

d = 3/2

a₂ = a+(2-1)d

a₂ = 5+3/2

a₂ = 13/2

a₃ = a+(3-1)d

a₃ = 5+2×3/2

a₃ = 8

Therefore, the missing terms are 13/2 and 8, respectively.

(iv) For the given A.P.,

a = −4 and

a₆ = 6

As we know, for an A.P.,

a_n = a +(n−1) d

Therefore, putting the values here,

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 the given A.P.,

a₂ = 38

a₆ = −22

As we know, for an A.P.,

a_n = 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 equation (i) from (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.