1. Sequences and series

arithmetic sequence = the next term adds/subtracts a constant difference from the last term

geometric sequence = the next term multiplies a constant ratio from the last term

series = the sum of the terms of a sequence

arithmetic sequence

• nth term → a + (n - 1)d

  • a = the first term

  • d = the common difference

• sum of the first n terms → (n/2)(2a + (n - 1)d)

geometric sequence

• nth term → ar^(n - 1)

  • aa = the first term

  • r d = the common ratio

• sum of the first n terms

  • a(r^n - 1) / (r -1)

  • a(1 - r^n) / (1 - r)

• sum to infinity

  • a / (1 - r)