Lesson

1.3 SEQUENCES AND SERIES




After completing this section, you should be able to:

  • understand what sequence is: \(4,9,14,19, \cdots \)
  • determine terms of series using general term: \( u_n = 4n+2 \)
  • find terms of arithmetic sequences: \( 3,5,7,9, \cdots \)
  • solve application problems involving arithmetic sequences
  • find terms of geometric sequences: \( 1, 2, 4, 8, \cdots \)
  • solve application problems involving geometric sequences
  • solve practical applications involving compound interest
  • write series in sigma notation: \( \displaystyle \sum_{n=1}^{10}{A_n} \)
  • determine the sum of arithmetic sequences:
    • \( S_n = \displaystyle \dfrac{n}{2}(u_1 + \ell) \)
    • \( S_n = \displaystyle \dfrac{n}{2}\Big[2u_1 + (n-1)d\Big] \)
  • determine the sum of geometric sequences:
    • \( S_n = \displaystyle \dfrac{u_1(r^n – 1)}{r-1} \)
    • \( S_n = \displaystyle \dfrac{u_1(1 – r^n)}{1 – r} \)
  • determine the sum of infinite series, so called sum to infinity: \( S_{\infty} = \displaystyle \dfrac{u_1}{1-r} \)