**(1) 5, 1, – 3, – 7, . . .**

**Solution:**

Given 5, 1, – 3, – 7, . . .

First term a_{1} = 5

Second term a_{2} = 1

Third term a_{3} = – 3

We know that d = a_{n + 1} – a_{n}

Thus, d = a_{2} – a_{1} = 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 a_{1} = 0.6

Second term a_{2} = 0.9

Third term a_{3} = 1.2

We know that d = a_{n + 1} – a_{n}

Thus, d = a_{2} – a_{1} = 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 a_{1} = 127

Second term a_{2} = 135

Third term a_{3} = 143

We know that d = a_{n + 1} – a_{n}

Thus, d = a_{2} – a_{1} = 135 – 127 = 8

Hence, the common difference d = 8 and first term is 127

**(4) 1/4, ¾, 5/4, 7/4, . . .**

**Solution:**