Question

Determine the explicit form of the arithmetic sequence given the following information.

a3 = 11 and a6 = 20

Answer 1

Explanation:

a3 = 11

a6 = 20

11 = a1 + (n - 1)*d

11 = a1 + (3 - 1)*d

11 = a1 + 2*d

20 = a1 + (n - 1)*d

20 = a1 + (6-1)*d

20 = a1 + 5*d

11 = a1 + 2d Subtract to get rid of the a1

9 = 3d Divide by 3

9/3 = d

d = 3

11 = a1 + 2*3

11 = a1 + 6 Subtract 6

11-6 = a1

a1 = 5

tn = 5 + (n - 1)^3

tn = 5 + 3n - 3

tn = 5 - 3 + 3n

tn = 2 + 3n