SAT Math: Repeating Sequences and Remainders

SAT Math: Repeating Sequences and Remainders


To solve problems using the remainder of integer division

In the refrigerator, left overs represent either an abundance of food...or the remains of a food that no one really liked in the first place. The math equivalent of left overs is the remainder of integer division which can be a useful tool in solving problems involving sequences.

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Consider the following questions:

  1. What is the remainder of 12581 when it is divided by 32?
  2. What is the 100th letter in the repeating sequence: A, B, C, D, E, F...
  3. For the repeating sequence of numbers: 1, -2, 3, -4, 5, -6, 1, -2, 3, -4, 5, -6, … what is the sum of the first 100 numbers?
  4. 179 people are seated in a room in rows of 17 seats per row.  Each row is filled before starting the next row.  How may people are in the last row.

Questions 2 - 4 involve repeating sequences and all of them involve the remainder of integer division.

Part 1: Computing the Remainder

Part 2: Determining the Nth Term in a Sequence

Part 3: Determining the Sum of a Repeating Sequence

Part 4: Using the Remainder to determine...the amount left over