Number Sequences Study Guide

Number sequences are sets of numbers that follow a specific pattern or rule. Understanding number sequences is an important concept in mathematics and can be found in various mathematical problems and real-life applications.

Types of Number Sequences

There are several types of number sequences, including:

Arithmetic Sequences

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. The constant difference is called the "common difference". The general form of an arithmetic sequence is: a, a + d, a + 2d, a + 3d, ...

Formula for the nth term of an arithmetic sequence:

a_n = a₁ + (n - 1)d

Geometric Sequences

A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the "common ratio". The general form of a geometric sequence is: a, ar, ar², ar³, ...

Formula for the nth term of a geometric sequence:

a_n = a₁ * r^(n-1)

Fibonacci Sequence

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. The sequence starts as: 0, 1, 1, 2, 3, 5, 8, 13, 21, ...

Square Number Sequence

The square number sequence is a sequence of numbers that are the squares of natural numbers. The sequence starts as: 1, 4, 9, 16, 25, 36, ...

Cubic Number Sequence

The cubic number sequence is a sequence of numbers that are the cubes of natural numbers. The sequence starts as: 1, 8, 27, 64, 125, ...

Study Tips for Number Sequences

Practice identifying patterns in number sequences.
Understand the difference between arithmetic and geometric sequences.
Memorize the formulas for the nth term of arithmetic and geometric sequences.
Solve a variety of sequence problems to reinforce your understanding.
Use visual aids and diagrams to help comprehend the sequences.

By understanding and practicing number sequences, you'll be better prepared to solve problems related to sequences and series in mathematics.

◂Math Worksheets and Study Guides Eighth Grade. Sequences

Arithmetic & Geometric Sequences

Worksheet/Answer key

General Sequences

The resources above cover the following skills:

Algebra (NCTM)

Understand patterns, relations, and functions.

Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.

Connections to the Grade 8 Focal Points (NCTM)

Algebra: Students encounter some nonlinear functions (such as the inverse proportions that they studied in grade 7 as well as basic quadratic and exponential functions) whose rates of change contrast with the constant rate of change of linear functions. They view arithmetic sequences, including those arising from patterns or problems, as linear functions whose inputs are counting numbers. They apply ideas about linear functions to solve problems involving rates such as motion at a constant speed.