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Understanding Geometric Sequences: Patterns of Numbers in Multiplying Sequence

Explore geometric sequences, find specific terms, calculate partial sums, know infinite sequences, and understand patterns in this informative guide. Discover examples and sums for better comprehension.

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Understanding Geometric Sequences: Patterns of Numbers in Multiplying Sequence

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  1. Sect 7.3: Geometric Sequence A geometric sequence is a pattern of numbers such that to get from one term to the next, you MULTIPLY by the same value.

  2. Examples of Geometric Sequences:

  3. Find the 10th term…20th term… 40th term…

  4. Geometric Sequence Ex: The first three terms are 3, 6, and 12.

  5. Ex: Find the 5th term, 8th term, and the nth term of the sequence: 27, 9, 3, 1, …

  6. Partial Sums of a Geometric Sequence Ex: Find the sum of the first five terms of the geometric sequence: 1, .3, .09, …

  7. Want A Job? Would you work for someone who offered you $0.01 for the first day’s wages and then doubled your daily wages for each day following for an entire month (31 days)?

  8. Sum of an Infinite Geometric Sequence Ex: Find the sum of ALL the terms of the geometric sequence: 4, 2, 1, …

  9. Sum of an Infinite Geometric Sequence

  10. Find the sum of the infinite series if it exists:

  11. Find the sum of the infinite series if it exists:

  12. Find the sum of the infinite series if it exists:

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