Question

What is the common difference of an AP in which T₁₈ −T₁₄ = 32?
(a) 8
(b) −8
(c) 4
(d) −4

Answer 1

(a) 8

The common difference of two terms is constant in an AP.
So, we have:
T₁₈ - T₁₇ = d ...(i)
T₁₇ - T₁₆ = d ...(ii)
T₁₆ - T₁₅ = d ...(iii)
T₁₅ - T₁₄ = d ...(iv)

On adding the four equations, we get:
T₁₈ - T₁₄ = 4d
However, ​T₁₈ - T₁₇ = 32
i.e., 4d = 32
⇒​ d = 8