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’