Given 2, 4, 6, 8, . . .

Here, the first term, a_{1} = 2

Second term, a_{2} = 4

And a_{3} = 6

Now, common difference = a_{2} – a_{1} = 4 – 2 = 2

Also, a_{3} – a_{2} = 6 – 4 = 2

Since, the common difference is same.

Hence the terms are in Arithmetic progression with common difference, d = 2.

**(2) 2, 5/2, 3, 7/3, . . .**

**Solution:**

**(3) – 10, – 6, – 2, 2, . . .**

**Solution:**

Given – 10, – 6, – 2,2, . . .

Here, the first term, a_{1} = – 10

Second term, a_{2} = – 6

a_{3} = – 2

Now, common difference = a_{2} – a_{1} = – 6 – (– 10) = – 6 + 10 = 4

Also, a_{3} – a_{2} = – 2 – (– 6) = – 2 + 6 = 4

Since, the common difference is same.

Hence the terms are in Arithmetic progression with common difference, d = 4.

**(4) 0.3, 0.33, .0333, . . .**

**Solution:**

Given 0.3, 0.33, 0.333, . . .

Here, the first term, a_{1} = 0.3

Second term, a_{2} = 0.33

a_{3} = 0.333

Now, common difference = a_{2} – a_{1} = 0.33 – 0.3 = 0.03

Also, a_{3} – a_{2} = 0.333 – 0.33 = 0.003

Since, the common difference is not same.

Hence the terms are not in Arithmetic progression

**(5) 0, – 4, – 8, – 12, . . .**

**Solution:**

Given 0, – 4, – 8, – 12, . . .

Here, the first term, a_{1} = 0

Second term, a_{2} = – 4

a_{3} = – 8

Now, common difference = a_{2} – a_{1} = – 4 – 0 = – 4

Also, a_{3} – a_{2} = – 8 – (– 4) = – 8 + 4 = – 4

Since, the common difference is same.

Hence the terms are in Arithmetic progression with common difference, d = – 4.

**(6) -1/5, -1/5, – 1/5, . . .**

**Solution:**

**(7) 3, 3 + √2, 3 + 2√2, 3 + 3√2, ….**

**Solution:**

Given

3, 3 + √2, 3 + 2√2, 3 + 3√2, ….

Here, the first term, a_{1} = 3

Second term, a_{2} = 3 + √2

a_{3} = 3 + 2√2

Now, common difference = a_{2} – a_{1} = 3 + √2 – 3 = √2

Also, a_{3} – a_{2} = 3 + 2√2 – (3 + √2) = 3 + 2√2 – 3 – √2 = √2

Since, the common difference is same.

Hence the terms are in Arithmetic progression with common difference, d = √2.

**(8) 127, 132, 137, . . .**

**Solution:**

Given 127, 132, 137, . . .

Here, the first term, a_{1} = 127

Second term, a_{2} = 132

a_{3} = 137

Now, common difference = a_{2} – a_{1} = 132 – 127 = 5

Also, a_{3} – a_{2} = 137 – 132 = 5

Since, the common difference is same.

Hence the terms are in Arithmetic progression with common difference, d = 5.