Given that an arithmetic sequence can be expressed as a linear function in the form f (x) = mx+b, write a linear function to describe the sequence {10,15,20,25,30,35 ... }

For this case we have:

m = (y2-y1) / (x2-x1)

m = (15-10) / (2-1)

m = 5/1

m = 5

Then,

y-yo = m (x-xo)

where,

(xo, yo) = (1, 10)

Substituting:

y-10 = 5 (x-1)

y = 5x - 5 + 10

y = 5x + 5

Answer:

a linear function to describe the sequence is:

y = 5x + 5