Answer:
uₙ₊₁ = uₙ + ¹/₂
Step-by-step explanation:
uₙ₊₁ = uₙ + d
u₈ = 3
u₁₀₀ = 49
We can establish the following:
u₉ = 3 + d
u₁₀ = (3 + d) + d = 3 + 2d
u₁₁ = (3 + 2d) + d = 3 + 3d
so...
u₈₊ₐ = 3 + ad
u₁₀₀ = u₈₊₉₂ = 3 + 92d
3 + 92d = 49
92d = 46
d = ¹/₂
∴ uₙ₊₁ = uₙ + ¹/₂
