Find the first term and common difference for each of the A.P.

(1) 5, 1, – 3, – 7, . . .

Solution:
Given 5, 1, – 3, – 7, . . .
First term a₁ = 5
Second term a₂ = 1
Third term a₃ = – 3
We know that d = a_{n + 1} – a_n
Thus, d = a₂ – a₁ = 1 – 5 = – 4
Hence, the common difference d = – 4 and first term is 5

(2) 0.6, 0.9, 1.2, 1.5, . . .

Solution:
Given 0.6, 0.9, 1.2, 1.5, . . .
First term a₁ = 0.6
Second term a₂ = 0.9
Third term a₃ = 1.2
We know that d = a_{n + 1} – a_n
Thus, d = a₂ – a₁ = 0.9 – 0.6 = 0.3
Hence, the common difference d = 0.3 and first term is 0.6

(3) 127, 135, 143, 151, . . .

Solution:
Given 127, 135, 143, 151, . . .
First term a₁ = 127
Second term a₂ = 135
Third term a₃ = 143
We know that d = a_{n + 1} – a_n
Thus, d = a₂ – a₁ = 135 – 127 = 8
Hence, the common difference d = 8 and first term is 127

(4) 1/4, ¾, 5/4, 7/4, . . .

Solution: