Explicit Models
Example 4

Find the 39th term of an arithmetic sequence whose first term is -3 and whose 24th term is 89.

Step 1. Substitute the values into the formula and solve for d.

an = a1+(n-1)d

a24 = -3+(24-1) d

92 = (23) d

89 = -3+(23) d

d = 4

Step 2. Substitute d = 4 and a = -3 and n = 39 into the formula and solve.

an = a1 + d(n - 1)

a39 = -3 + 4(39 - 1)

a39 = -3 + 4(38)

a39 = -3 + 152

a39 = 149