Answer:

(i) 

Arithmetic Progression (AP) whose common difference is = a_n – a_n-1 where n > 0

Consider,

a = a₁ = 1, a₂ = 4 …

Common difference, d = a₂ – a₁ = 4 – 1 = 3

Finding a_n

a_n = a + (n-1) d

= 1 + (n-1) 3

= 1 + 3n – 3

= 3n – 2

When n = 10,

a₁₀ = 3(10) – 2

= 30 – 2

= 28

10^th term is 28.

(ii) 

Arithmetic Progression (AP) whose common difference is = a_n – a_n-1 where n > 0

Consider,

a = a₁ = √2, a₂ = 3√2 …

Common difference, d = a₂ – a₁ = 3√2 – √2 = 2√2

Find a_n

a_n = a + (n-1) d

= √2 + (n – 1) 2√2

= √2 + 2√2n – 2√2

= 2√2n – √2

When n = 18,

a₁₈ = 2√2(18) – √2

= 36√2 – √2

= 35√2

10^th term is 35√2