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How Do You Write a Rule for a Geometric Sequence?

Write a rule for the geometric sequence 2, 4, 8, 16, ..., then use it to find the 6th, 9th, and 15th terms.

Summary

  1. The nth term means a specific term in the sequence
  2. So for the 6th term, 'n' would be 6
  3. 'a' stands for the first term in the geometric sequence
  4. 'A(n)' is the value of the nth term
  5. 'r' stands for the common ratio
  6. The common ratio is the number we multiply each term by to get the next term in the sequence
  7. This formula helps quickly find a specific term in a geometric sequence

Notes

    1. The nth term means a specific term in the sequence
    2. In this example we want to find the 6th, 9th, and 15th terms in the sequence
    3. So 6, 9, and 15 are possible values for 'n'
    1. The nth term means a specific term in the sequence
    2. In this example we want to find the 6th, 9th, and 15th terms in the sequence
    3. So 6, 9, and 15 are possible values for 'n'
    4. This formula helps quickly find a specific term in a geometric sequence
    1. 'a' stands for the first term in the geometric sequence
    2. The first term in our sequence is 2
    3. So a=2
    1. The common ratio is the constant that we multiply each term in a sequence by to get the next term
    1. 2 and 4 are the first two numbers in our sequence
    2. Any two consecutive terms in a geometric sequence will give you the same ratio
    3. That's why it's called a COMMON ratio
    1. The common ratio is the constant that we multiply each term in a sequence by to get the next term
    2. The ratio needs to be the same between EACH PAIR of consecutive terms in the sequence to be a common ratio
    1. We can check some other pairs of consecutive terms in the sequence to make sure we get the same ratio each time
    2. We get 2 for each pair, so 2 is the common ratio
    1. 'A(n)' is the value of the nth term
    2. 'a' is the first term in the sequence, which is 2
    3. 'r' is the common ratio, which is also 2
    4. 'n' is the position of a specific term in the sequence: so for the 6th term, 'n' would be 6
    5. We can plug in any number into this function for 'n' to get the value for that term
    1. 'n' is the position of a specific term in the sequence: so for the 6th term, 'n' would be 6
    1. 'n' is the position of a specific term in the sequence
    2. For the 6th term in the sequence, 'n' must be 6
    1. Plug in 6 for 'n' and solve to find the value of the 6th term
    2. The 6th term in the sequence is 64
    1. 'n' is the position of a specific term in the sequence
    2. For the 9th term in the sequence, 'n' must be 9
    1. Plug in 9 for 'n' and solve to find the value of the 9th term
    2. The 9th term in the sequence is 512
    1. 'n' is the position of a specific term in the sequence
    2. For the 15th term in the sequence, 'n' must be 15
    1. Plug in 15 for 'n' and solve to find the value of the 15th term
    2. The 15th term in the sequence is 32,768