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Arithmetic Sequence Defined
- Constant Difference Between Each Term in Order in the Sequence
- Consecutive Integers, Odds, or Multiples are Arithmetic Sequences
- Median of Sequence = Average of Sequence
- Can Solve for Value of Any Term with Value of Single Term and Difference
- a_n = a_1 + (n - 1) × d
- d : Constant Difference Between Terms
Geometric Sequence Defined
- Constant Ratio Between Terms
- Can Solve for Value of Any Term with Value of First Term and Multiplier
- a_n = a_1 × r (n - 1)
- r : Constant Ratio Between Terms
GMAT Quantitative Patterns
- Can be Creatively Tested
- Often Related to Sequences and Sets
- Require Recognition Over Calculation
- Frequently Seek Sums, Averages, or Terms
Strategic Implications
- Sometimes Identifiable by Questions Seeking Non-Specific Values
- Ranges and Approximations
- Write Out All Steps Before Beginning Calculations
- Avoid Auto-Processing Arithmetic to Notice Possible Patterns
- Carefully Evaluate Information to Logically Solve
Sequences and Patterns Process
Step 1 - Set up Scratch Pad for Problem
- Note Sought Value and Format of the Choices to Inform Problem Solving or Data Sufficiency Processes
Step 2 - Carefully Read Problem and Articulate the Defined Sequence
- Beware of Confusing Term Number for Term Value
- Write Terms Fully without Immediately Calculating
Step 3 - Consider Best Approach for Solving
- Take the Technical Path to Solving if You Can
- Abandon Technical Approach in Favor of Logical Estimation if You can Identify Efficiencies Through Pattern Recognition