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SAT Math: Repeating Sequences and Remainders

Author: Morris Goldstein

Introduction

Consider the following questions:

What is the remainder of 12581 when it is divided by 32?
What is the 100th letter in the repeating sequence: A, B, C, D, E, F...
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?
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