Write an A.P. whose first term is a and common difference is d in each

1.	Write an A.P. whose first term is a and common difference is d in each of the following.i. a = -1.25, d = 3 ii. a = 6, d = -3 iii. a = -19, d = -4
Answer» i. a = -1.25, d = 3 …[Given] t₁ = a = -1.25 t₂ = t₁ + d = – 1.25 + 3 = 1.75 t₃ = t₂ + d = 1.75 + 3 = 4.75 t₄ = t₃ + d = 4.75 + 3 = 7.75 ∴ The required A.P. is -1.25, 1.75, 4.75, 7.75,… ii. a = 6, d = -3 …[Given] ∴ t₁ = a = 6 t₂ = t₁ + d = 6 – 3 = 3 t₃ = t₂ + d = 3 – 3 = 0 t₄= t₃ + d = 0- 3 = -3 ∴ The required A.P. is 6, 3, 0, -3,… iii. a = -19, d = -4 …[Given] t₁ = a = -19 t₂ = t₁ + d = -19 – 4 = -23 t₃ = t₂ + d = -23 – 4 = -27 t₄ = t₃ + d = -27 – 4 = -31 ∴ The required A.P. is -19, -23, -27, -31, …

Write an A.P. whose first term is a and common difference is d in each of the following.i. a = -1.25, d = 3 ii. a = 6, d = -3 iii. a = -19, d = -4

Answer»

i. a = -1.25, d = 3 …[Given]

t₁ = a = -1.25

t₂ = t₁ + d = – 1.25 + 3 = 1.75

t₃ = t₂ + d = 1.75 + 3 = 4.75

t₄ = t₃ + d = 4.75 + 3 = 7.75

∴ The required A.P. is -1.25, 1.75, 4.75, 7.75,…

ii. a = 6, d = -3 …[Given]

∴ t₁ = a = 6

t₂ = t₁ + d = 6 – 3 = 3

t₃ = t₂ + d = 3 – 3 = 0

t₄= t₃ + d = 0- 3 = -3

∴ The required A.P. is 6, 3, 0, -3,…

iii. a = -19, d = -4 …[Given]

t₁ = a = -19

t₂ = t₁ + d = -19 – 4 = -23

t₃ = t₂ + d = -23 – 4 = -27

t₄ = t₃ + d = -27 – 4 = -31

∴ The required A.P. is -19, -23, -27, -31, …