For the AP - 3, - 7, - 11, … can we find directly a₃₀ - a₂₀ without actually finding a₃₀ and a₂₀ reason for your answer.

Question

For the AP - 3, - 7, - 11, … can we find directly a 30 - a 20 without actually finding a 30 and a 20 reason for your answer.

Philoid · Accepted Answer

True

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

For the AP - 3, - 7, - 11, … can we find directly a30 - a20 without actually finding a30 and a20 reason for your answer.