The sum of a geometric sequence

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Presentation transcript:

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

Sum of a Finite Geometric Sequence Series notation

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

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

Example 4-2a

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

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

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

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