If an denotes the nth term of the AP 2, 7, 12, 17, …, find the value

1.	If an denotes the nth term of the AP 2, 7, 12, 17, …, find the value of (a30 – a20).
Answer» Given AP is 2, 7, 12, 17,…….. Here, a = 2, d = 7 – 2 = 5 Now, a_n = a + (n – 1) d = 2 + (n – 1) 5 = 5n – 3 a₃₀ = 2 + (30 – 1) 5 = 2 + 145 = 147 and a₂₀ = 2 + (20 – 1) 5 = 2 + 95 = 97 a₃₀ – a₂₀ = 147 – 97 = 50

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

Answer»

Given AP is 2, 7, 12, 17,……..

Here, a = 2, d = 7 – 2 = 5

Now,

a_n = a + (n – 1) d = 2 + (n – 1) 5 = 5n – 3

a₃₀ = 2 + (30 – 1) 5 = 2 + 145 = 147 and

a₂₀ = 2 + (20 – 1) 5 = 2 + 95 = 97

a₃₀ – a₂₀ = 147 – 97 = 50