If a_n denotes the nth term of the AP 3, 8, 13, 18, ... then what is the value of (a₃₀ - a₂₀)?

Here, First term = a = 3

Common difference = d = 8 - 2 = 5

To find: a₃₀ – a₂₀

So, n^th term is given by:

a_n = a + (n - 1)d

∴ 30^th term is:

a₃₀ = 3 + (30 - 1) × 5

= 3 + 145

= 148

Now, 20^th term is:

a₂₀ = 3 + (20 - 1) × 5

= 3 + 95

= 98

Now, (a₃₀ – a₂₀) = 148 - 98

= 50

∴ (a₃₀ – a₂₀) = 50