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n-th Term of an Arithmetic Sequence

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n-th Term of an Arithmetic Sequence

Study Guide

Key Definition

The n-th term of an arithmetic sequence can be found using the formula $a_n = a_1 + (n - 1) \times d$

Important Notes

The first term is denoted as $a_1$
The common difference is denoted as $d$
The formula $a_n = a_1 + (n - 1) \times d$ is used to find the n-th term
Each term increases or decreases by the common difference $d$
Ensure n is a positive integer when finding the n-th term

Mathematical Notation

$a_n$ is the n-th term

$a_1$ is the first term

$d$ is the common difference

$n$ is the term number

Remember to use proper notation when solving problems

Why It Works

This formula works because each term in an arithmetic sequence is generated by adding the common difference $d$ to the previous term.

Remember

The key formula is $a_n = a_1 + (n - 1) \times d$

Quick Reference

n-th Term Formula:$a_n = a_1 + (n - 1) \times d$

Understanding n-th Term of an Arithmetic Sequence

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

The formula $a_n = a_1 + (n - 1) \times d$ helps you find any term in a sequence easily.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the 5th term in the sequence if $a_1 = 3$ and $d = 2$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

If you save $5$ dollars each week, how much will you save in the 20-th week?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Consider the sequence where $a_1 = 7$ and $d = -3$. What pattern emerges?

Challenge Quiz

Single Choice Quiz

Advanced

If $a_1 = 10$ and $d = 4$, what is the 50th term?

Recap

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