If a_n denotes the nth term of the AP 2, 7, 12, 17, ..., find the value of (a₃₀ – a₂₀).

Here, First term = a = 2

Common difference = d = 7 - 2 = 5

To find: a₃₀ – a₂₀

So, n^th term is given by:

a_n = a + (n - 1)d

∴ 30^th term is:

a₃₀ = 2 + (30 - 1) × 5

= 2 + 145

= 147

Now, 20^th term is:

a₂₀ = 2 + (20 - 1) × 5

= 2 + 95

= 97

Now, (a₃₀ – a₂₀) = 147 - 97

= 50

∴ (a₃₀ – a₂₀) = 50