nth arithmetic algebra

Question

Use a system of two equations in two variables, a, and d, to write a formula for the general term (the nth term) of the arithmetic sequence whose sixth term, a6, is 3 and whose ninth term, a9, is 9.

Answer 1

Use the formula a_n = a₁ + (n-1)d with n = 6 and n = 9 to get:

3 = a₁ + 5d

9 = a₁ + 8d

Then solve for a₁ and d.