The terms in two positions of some arithmetic sequences are given below. Write the first five terms of each:

i) 3rd term 34

6th term 67

ii) 3rd term 43

6th term 76

iii) 3rd term 2

5th term 3

iv) 4th term 2

7th term 3

v) 2nd term 5

5^th term 2

i) a₃ = 34

a₆ = 67

a₃ = a + 2d and a₆ = a + 5d

Solving,a₆ = a₃ + 3d

∴ d = 11

a₂ = 34-11 = 23

a = 23-11 = 12

a₄ = 34 + 11 = 45

a₅ = 45 + 11 = 56

First 5 terms are 12,23,34,45 and 56

ii) a₃ = 43

a₆ = 76

a₃ = a + 2d and a₆ = a + 5d

Solving,a₆ = a₃ + 3d

∴ d = 11

a₂ = 43-11 = 32

a = 32-11 = 21

a₄ = 43 + 11 = 54

a₅ = 54 + 11 = 65

First 5 terms are 21,32,43,54 and 65

iii) a₃ = 2

a₅ = 3

a₃ = a + 2d and a₅ = a + 4d

Solving, a₅ = a₃ + 2d

d = 0.5

a₂ = 2-0.5 = 1.5

a = 1.5-0.5 = 1

a₄ = 2 + 0.5 = 2.5

First 5 terms are 1,1.5,2,2.5 and 3

iv) a₄ = 2

a₇ = 3

a₄ = a + 3d

a₇ = a + 6d

Solving,a₇ = a₄ + 3d

d =

a₃ = =

a₂ = =

a = = 1

a₅ = 2 + =

First 5 terms are 1,4/3,5/3,2 and 7/3

v) a₂ = 5

a₅ = 2

a₂ = a + d

a₅ = a + 4d

Solving,a₅ = a₂ + 3d

d = -1

a = 5-(-1) = 6

a₃ = 5-1 = 4

a₄ = 4-1 = 3

a₅ = 3-1 = 2

First 5 terms are 6,5,4,3,2.

Hence solved.