Question

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 1

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