Solving Sequence Problems

Geometric Sequences

  • In a geometric sequence, the ratio between consecutive is constant
    • Here are twp examples of geometric sequences:
    • 3, 9, 27, 81, 243
    • 2, 4, 8, 16, 32

Sequences and equations

  • You can use the nth term or the term-term rule of a sequence to write an equation
  • This sequence has term-to-term rule ‘multiply by 2 then add 4’
    • 11, 25, 53
    • x2 + a x2 +a
    • So 2x11 + a = 25 and a=3
    • You could use this information to find the next term in the sequence

Problem solved

  • Work out what information you need to solve the problem
  • You can’t find the first term until you known that value of k
  • You know two consecutive terms so you can solve an equation to find the value of k

Fibonacci sequence

  • The rule for generating this sequence is ‘add two consecutive terms to get the next term’
    • 2,3,5,8,13,21