N-th Term Of An Arithmetic Sequence - Varsity Tutors

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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 numberRemember 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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Beginner Explanation

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

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

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

A$11$B$9$C$13$D$15$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

If you save $5$ dollars each week, how much will you save in the 20-th week?Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

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

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

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

A$206$B$200$C$210$D$214$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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