1. The sum of a geometric sequence
11.4: Geometric Series:
The sum of a geometric sequence

2. Sum of a Finite Geometric Sequence
Series notation

3. Answer: Going back 8 generations, a person would have 510 ancestors.
Genealogy How many direct ancestors would a person have after 8 generations?
Counting two parents, four grandparents, eight great- grandparents, and so on gives you a geometric series with
Sum formula
Use a calculator.
Answer: Going back 8 generations, a person would have 510 ancestors.
Example 4-1a

4. Evaluate
Method 1
Find the terms by replacing n with 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Then add.
Example 4-2a

5. Example 4-2a

6. Since the sum is a geometric series, you can use the formula
Method 2
Since the sum is a geometric series, you can use the formula
Evaluate
Sum formula
Simplify.
Answer: The sum of the series is 12,285.
Example 4-2a

7. Find the sum of a geometric series for which
Since you do not know the value of n, use the formula
Alternate Formula
Example 4-3a

8. Answer: The sum of the series is 6666.
Alternate sum formula
Simplify.
Answer: The sum of the series is 6666.
Example 4-3a

9. Find a1 in a geometric series for which and
Sum formula
Subtract.
Divide each side by –255.
Answer: The first term of the series is 3.
Example 4-4a