1.5 SERIES - ARITHMETIC AND GEOMETRIC

Cards (15)

  • Sₙ - Sum of all n terms
  • Write the formula for Sₙ in an Arithmetic Series.
    Note:
    Write subscript like aₙ as [an]. For example, a₅ we write it as a5.
    For Fractions, instead of writing ½, write 1/2 instead.
    For Exponents, we use [^]. For example, a⁴ can be written as a^4.

    Sn = n/2(a1 + an)
  • Find the 20th term and the sum of the first 20 terms of the arithmetic sequence -7, - 4, -1, 2, …
    • a1 = -7
    • n = 20
    • d = 3
    • an = 50
    • Sn = 430
  • Find the 25th term and the sum of the first 25 terms of the arithmetic sequence 12, 16, 20, 24, …
    • a1 = 12
    • n = 25
    • d = 4
    • an = 108
    • Sn = 1500
  • Find four arithmetic means between 16 and 76.
    • a1 = 16
    • n = 6
    • an = 76
    • d = 12
    • 16, 28, 40, 52, 64, 76
  • Find the sum of the first 30 terms of the arithmetic sequence 11, 16, 21, 26, …
    • a1 = 11
    • n = 30
    • d = 5
    • an = 156
    • Sn = 2505
  • Write the formula for Sn in a Geometric Sequence.
    Note:
    Write subscript like aₙ as [an]. For example, a₅ we write it as a5.
    For Fractions, instead of writing ½, write 1/2 instead.
    For Exponents, we use [^]. For example, a⁴ can be written as a^4.
    Sn = a1(1-r^n)/1-r
  • Find the sum of the first 12 terms of the geometric sequence 3, -9, 27, -81, 243, ...
    a1 = 3
    n = 12
    r = -3
    Sn = -398580
  • Find S10 of the Geometric Sequence -1/2, -1, -2, -4...
    • a1 = -1/2
    • n = 10
    • r = 2
    • Sn = -511.5 or -511 1/2
  • Arithmetic Series - The sum of first n terms in an arithmetic sequence.
  • Finite Geometric Series - The sum of first 𝑛 terms in a geometric sequence.
  • Infinite Geometric Series - The sum of infinite terms of a geometric sequence.
  • Formula for infinite geometric series
    Note:
    Write subscript like aₙ as [an]. For example, a₅ we write it as a5.
    For Fractions, instead of writing ½, write 1/2 instead.
    For Exponents, we use [^]. For example, a⁴ can be written as a^4.
    S∞ = a1/1-r
  • Find the sum of the Geometric Sequence: 1, 1/2, 1/4, 1/8, 1/16, ...
    • a1 = 1
    • r = 1/2
    • S∞ = 2
  • Find the sum of the Geometric Sequence: 2, 2/3, 2/9, 2/7...
    • a1 = 2
    • r = 1/3
    • S∞ = 3