1.5 SERIES - ARITHMETIC AND GEOMETRIC

• 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