1.4 GEOMETRIC SEQUENCE, MEANS

    Cards (13)

    • 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