Find the first term and common difference for each of the A.P.i. 5, 1

1.	Find the first term and common difference for each of the A.P.i. 5, 1, -3, -7, ...ii. 0.6, 0.9, 1.2, 1.5, ...iii. 127, 135, 143,151, ...iv. 1/4, 3/4, 5/4, 7/4, ....
Answer» i. The given A.P. is 5, 1,-3,-7,… Here, t₁= 5, t₂= 1 ∴ a = t₁ = 5 and d = t_1^-t₂= 1 – 5 = -4 ∴ first term (a) = 5, common difference (d) = -4 ii. The given A.P. is 0.6, 0.9, 1.2, 1.5,… Here, t₁ = 0.6, t₂ = 0.9 ∴ a = t₁ = 0.6 and d = t₂ – t₁ = 0.9 – 0.6 = 0.3 ∴ first term (a) = 0.6, common difference (d) = 0.3 iii. The given A.P. is 127, 135, 143, 151,… Here, t₁ = 127, t₂ = 135 ∴ a = t₁ = 127 and d = t₂ – t₁ = 135 – 127 = 8 ∴ first term (a) = 127, common difference (d) = 8 iv The given A,P is 1/4, 3/4, 5/4, 7/4, ... Here, t₁ = 1/4, t₂ = 3/4 ∴ a = t₁ = 1/4 and d = t₂ - t₁ = 3/4 - 1/4 = 2/4 = 1/2 ∴ first terms (a) = 1/4, common diference (d) = 1/2

Find the first term and common difference for each of the A.P.i. 5, 1, -3, -7, ...ii. 0.6, 0.9, 1.2, 1.5, ...iii. 127, 135, 143,151, ...iv. 1/4, 3/4, 5/4, 7/4, ....

Answer»

i. The given A.P. is 5, 1,-3,-7,…

Here, t₁= 5, t₂= 1

∴ a = t₁ = 5 and

d = t_1^-t₂= 1 – 5 = -4

∴ first term (a) = 5,

common difference (d) = -4

ii. The given A.P. is 0.6, 0.9, 1.2, 1.5,…

Here, t₁ = 0.6, t₂ = 0.9

∴ a = t₁ = 0.6 and

d = t₂ – t₁ = 0.9 – 0.6 = 0.3

∴ first term (a) = 0.6,

common difference (d) = 0.3

iii. The given A.P. is 127, 135, 143, 151,…

Here, t₁ = 127, t₂ = 135

∴ a = t₁ = 127 and

d = t₂ – t₁ = 135 – 127 = 8

∴ first term (a) = 127,

common difference (d) = 8

iv The given A,P is 1/4, 3/4, 5/4, 7/4, ...

Here, t₁ = 1/4, t₂ = 3/4

∴ a = t₁ = 1/4 and

d = t₂ - t₁ = 3/4 - 1/4 = 2/4 = 1/2

∴ first terms (a) = 1/4,

common diference (d) = 1/2