geometric sequences grade 10

• Geometric sequence


  A sequence of non-zero numbers where each term is found by multiplying the previous term by a fixed number called the common ratio
• Finding the next terms in a geometric sequence

  1. Find the common ratio (a_2/a_1)

  2. Multiply the previous term by the common ratio to get the next term
• Geometric sequence


  • 1, 2, 4, 8
• Common ratio


  The fixed number used to multiply each term to get the next term in a geometric sequence
• Finding the common ratio

  a_2/a_1
• Finding the common ratio

  • 1 to 2 is 2
  • 2 to 4 is 2
  • 4 to 8 is 2
• Finding the 4th, 5th and 6th terms

  1. 4th term = 3rd term * common ratio

  2. 5th term = 4th term * common ratio

  3. 6th term = 5th term * common ratio
• The formula to find the common ratio is a_2/a_1
• Geometric means and geometric series will be discussed in the next part of the video
• Sequence


  An ordered list of numbers
• Sequence


  • Finite - has a last term
  • Infinite - no last term
• Term


  Each number in a sequence
• General term


  A mathematical expression or rule for generating the sequence
• Finding general term


  1. Identify pattern

  2. Substitute values into formula
• General term formula


  a_n = n^2 - 3

  a_n = (-1)^n / (2n - 1)

  a_n = n^3

  a_n = 1/n
• Alternating sign sequences use (-1)^n in the general term
• Sequences with common differences use linear expressions in the general term
• Sequences with common ratios use exponential expressions in the general term
• Sequences with polynomial terms use polynomial expressions in the general term
• Sequence


  An ordered list of numbers
• Sequence


  • Finite - has a last term
  • Infinite - no last term
• Term


  Each number in a sequence
• General term


  A mathematical expression or rule for generating the terms of a sequence
• Finding general term


  1. Identify pattern

  2. Substitute values into formula

  3. Verify formula matches first few terms
• General term formula


  a_n = n^2 - 3

  a_n = (-1)^n / (2n - 1)

  a_n = 5n

  a_n = n(n+1)/2
• Sequences can have terms that alternate in sign
• Even exponents in general term formula result in positive terms, odd exponents result in alternating signs
• General term formulas can represent sequences of perfect squares, cubes, fractions, etc.