In each of the arithmetic sequences below, some terms are missing and their positions are marked with ∘. Find them.

i) 24, 42, ∘, ∘, … ii) ∘, 24, 42, ∘, …

iii) ∘, ∘, 24, 42, … iv) 24, ∘, 42, ∘, …

v) ∘, 24, ∘, 42, … vi) 24, ∘, ∘, 42, …

Let a = first term of arithmetic sequence

a_{2 ,} a_{3 ,} a_4… are second, third, fourth terms and so on

d = common difference

i) Here, a = 24

a₂ = 42

d = 42-24 = 18

a₃ = 42 + 18 = 60

a₄ = 60 + 18 = 78

ii) Here, a₂ = 24

a₃ = 42

d = 42-24 = 18

a = a₂ – d = 24-18 = 6

a₄ = 42 + 18 = 60

iii) Here, a₃ = 24

a₄ = 42

d = a₄ – a₃ = 42-24 = 18

a₂ = 24 – 18 = 6

a = 6-18 = -12

iv) Here, a = 24

a₃ = 42

a₃ = a + 2d

Solving, d = 9

∴ a₂ = 24 + 9 = 33

a₄ = 42 + 9 = 51

v) Here, a₂ = 24

a₄ = 42

a₄ = a + 3d …(eq)1

and,a₂ = a + d …(eq)2

Eliminating a;

d = 9

a = 24-9 = 15

a₃ = 24 + 9 = 33

vi) Here, a = 24

a₄ = 42

a_{4 =} a + 3d

Solving, d = 6

a₂ = 24 + 6 = 30

a₃ = 30 + 6 = 36

Hence, all the answers are found.