1.4 GEOMETRIC SEQUENCE, MEANS

• Geometric Sequence - A sequence in which a constant (r) can be multiplied to each term to get the next term.
• Common Ratio - This is called the constant (r)
• To find the common ratio (r), divide any term from one that follows it.
• Formula for Geometric Sequence

  (Note: Write subscript like aₙ as [an]. For example, a₅ we write it as a5. For exponents, we use [^]. For Example, a⁴ we write it as a^4.

  
  

  an = a1r^n-1
• Find the 9th term of the geometric sequence: 5, 15, 45

  • a1 = 5
  • n = 9
  • r = 3
  • a9 = 32805
• Find the 5th term of the geometric sequence: 20, -10, 5

  • a1 = 20
  • n = 5
  • r = -1/2
  • a5 = 5/4
• Find the 1st term of the geometric sequence

  • a7 = 15625
  • n = 7
  • r = 5
  • a1 = 1
• Find the 1st term of the geometric sequence

  • a4 = -40
  • n = 4
  • r = -2
  • a1 = 5
• Find the common ratio

  • a1 = 7
  • n = 4
  • a4 = 875
  • r = 5
• Find r of the sequence

  a1 = -5

  n = 4

  a4 = 1080

  r = -6
• Geometric means - The terms between 𝑎1 and 𝑎n of a geometric sequence.
• Insert two geometric means between a1 = 7 and a4 = 875.

  • a1 = 7
  • n = 4
  • r = 5
  • 7, 35, 175, 875
• Insert two geometric means between a1 = -5 and a4 = 1 080.

  a1 = -5

  n = 4

  a4 = 1080

  r = -6

  -5, 30, -180, 1080