Geometric

Explicit Models

Example 4

Find the nth and the 26th terms of the geometric sequence with a5 = 5/4 and a12 = 160.

Step 1. These two terms are 12 - 5 = 7 places apart. Based on the definition of a geometric sequence stated earlier in this unit, a12 = ( a5 )( r7 ). Use this equation to solve for the value of the common ratio, r.

explicit_ex4-1

Step 2. Using information from one of the given terms, substitute and solve for a1.

explicit_ex4-2


Step 3. Substitute a1 into the formula.

explicit_ex4-3

Step 4. Find the 26th term.

Substitute n = 26 into the formula and solve.

explicit_ex4-4