Geometric Sequence
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1. The document instructs readers to fold a square piece of paper into quarters and record the resulting areas in a table after each fold. 2. It starts with a square of area 64 square units and folds the corners into the center, halving the side length and quartering the area each time. 3. The reader is to repeat this folding process three times and record the resulting areas in a provided table.
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Geometric Sequence
- 2. Do the activity with a partner. One of you will perform the paper folding while the other will do the recording in the table. 1. Start with a big square from a piece of paper. Assume the area of the square is 64 square units. 2. Fold the four corners to the center of the square and find the area of the resulting square. 3. Repeat the process three times and record the results in the table below. Square 1 2 3 Area
- 3. Geometric Sequence is a sequence where each term after the first is obtained by multiplying the preceding term by a nonzero constant called the common ratio.
- 4. Problem: What are the first 5 terms of a geometric sequence whose first term is 2 and whose common ratio is 3? Given the first term a1 and the common ratio r of a geometric sequence, the nth term of a geometric sequence is _
- 5. Example: What is the 10th term of the geometric sequence 8, 4, 2, 1, …? Solution: The 10th term is 1 64
- 6. Geometric Mean A geometric mean is a number inserted between any two given numbers so that the terms form geometric sequence.
- 7. Example: Insert two geometric means between 3 and 192.
- 8. Solution: The geometric means between 3 and 192 are 12 and 48.
- 9. Sum of Geometric Sequence The formula of the first n terms of a geometric sequence is
- 10. Examples: A. Find the sum of the seven terms of geometric sequence 3, 6, 12, 24. Solution:
- 11. B. Find the sum of the geometric sequence 40, -20, 10, -5, 5/2, -5/4. Solution:
- 12. Quiz 1. Write the first five terms of a geometric sequence whose first term is 2 and whose common ratio is 3. 2. Insert three geometric means between -3 and 96. 3. Find the sum of the first 5 terms of the geometric sequence whose first term is 128 and its common ratio is one- half.