Show that each of the progressions given below is an AP. Find the first term, common difference and next term of each.

Question

Philoid · Accepted Answer

Here, T₂ - T₁ = (-5/6) - (-1) = 1/6

T₃ - T₂ = (-2/3) - (-5/6) = 1/6

T₄ - T₃ = (-1/2) - (-2/3) = 1/6

Since the difference between each consecutive term is same, ∴ the progression is an AP.

So, first term = - 1

Common difference = (-5/6) - (-1) = 1/6

Next term = T₅ = T₄ + d

= (-1/2) + (1/6)

= (-2/6)

= (-1/3)