Formulas

Things one must know:

• Plug-In formulas: simply write the equation down, plug in the numbers carefully, and solve for the required unknown. Be sure to write the formula as a part of an equation.
• Strange Symbol formulas: The symbol is irrelevant. All that is important is that you carefully follow each step in the procedure that the symbol indicates. Watch out for symbols that invert the order of an operation.
• Formula problems that involve unspecified amounts should be solved by picking smart numbers for the unspecified variables.
• Sequences are defined by function rules: each term is a function of its place in the sequence. 
• You must be given the rule in order to find a particular number in a sequence. 
• Recursive formulas - each item of a sequence is defined in terms of the value of the previous items in the sequence. You need to be given the recursive rule and also the value of one of the items in the sequence to solve for the values of a recursive sequence. The subscript n - 1 means "the previous term", and the subscript n means "this term.
  
• Linear sequence, the difference between successive terms is always the same.
  Direct formula: Sn = kn + x, where k is the constant difference between successive terms and x is some other constant.
  Recursive formula: Sn = Sn₋₁ + k and S₁ = k + x
  Compute the difference between two terms to find k, you can then solve for x.
  
• Exponential sequence, each term is equal to the previous term times a constant k, the ratio between successive terms is always the same.
  Direct formula: Sn = x(kⁿ), where x and k are real numbers.
  Recursive formula: Sn = kSn₋₁ and S₁ = xk
  You can find k by combing equations, then solve for x.
  
• If a problem seems to require too much computation, look for a pattern to find an easier way to solve it.