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Arithmetic Sequences

Understanding arithmetic sequences is crucial for solving related problems on the GRE exam, focusing on identifying patterns, formulating the nth term, and applying this knowledge to solve practice problems.
  • An arithmetic sequence is defined by adding a constant to each term to get the next term, with examples including consecutive integers, odds, evens, and multiples of a number.
  • The nth term of an arithmetic sequence can be found using the formula a sub n = a sub 1 + (n - 1) * d, where d is the common difference.
  • Understanding the derivation of the formula for the nth term is emphasized over rote memorization for deeper comprehension and application.
  • Practice problems illustrate the application of the formula to find specific terms in a sequence and to solve for unknowns given certain terms.
  • The concept of evenly spaced lists as arithmetic sequences extends to sets of numbers that, when divided by a divisor, yield a fixed remainder.
Introduction to Arithmetic Sequences
Formulating the nth Term
Generalizing the Formula
Applying the Formula: Practice Problems