Question

For the AP: –3, –7, –11, ..., can we find directly a₃₀ – a₂₀ without actually finding a₃₀ and a₂₀? Give reasons for your answer.

Answer 1

Given:

First term, a = – 3

Common difference, d = a₂ – a₁ 

= – 7 – (– 3)

= – 4

a₃₀ – a₂₀ = a + 29d – (a + 19d)

= 10d

= – 40

It is so because difference between any two terms of an AP is proportional to common difference of that AP.