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

Question

Show that each of the progressions given below is an AP. Find the first term, common difference and next term of each. 9, 15, 21, 27, ...

Philoid · Accepted Answer

Here, T₂ - T₁ = 15 - 9 = 6

T₃ - T₂ = 21 - 15 = 6

T₄ - T₃ = 27 - 21 = 6

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

So, first term = 9

Common difference = 15 - 9 = 6

Next term = T₅ = T₄ + d = 27 + 6 = 33