The 8th term of an arithmetic sequence is 3 and the 100th term is 49. What is the recursive formula for the sequence?

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

step-by-step explanation:

compare

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have