Which of the Following Is an Arithmetic Sequence? (Brainly Guide): Complete Explanation with Examples

Mathematics is full of patterns, and one of the most common patterns students encounter is the arithmetic sequence. If you searched “Which of the following is an arithmetic sequence Brainly“, you are probably trying to solve a homework question or prepare for an exam. Understanding arithmetic sequences is easier than it seems once you know the simple rule that defines them. Instead of memorizing answers, learning the concept will help you solve nearly every arithmetic sequence question you encounter in school.

Arithmetic sequences appear in middle school, high school, college entrance exams, and standardized tests because they teach students how numbers change in a predictable way. These sequences also have practical applications in finance, engineering, computer science, and everyday problem-solving. Learning how to recognize an arithmetic sequence is therefore a valuable mathematical skill that extends beyond the classroom.

What Is an Arithmetic Sequence?

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms remains constant. This constant difference is known as the common difference (d).

For example:

• 2, 5, 8, 11, 14
• 10, 15, 20, 25
• 50, 45, 40, 35

Each sequence changes by exactly the same amount every time.

How to Identify an Arithmetic Sequence

Follow these simple steps:

Step 1: Find the Difference

Subtract each term from the next term.

Example:

5, 8, 11, 14

• 8 − 5 = 3
• 11 − 8 = 3
• 14 − 11 = 3

Since every difference equals 3, this is an arithmetic sequence.

Example 2

4, 9, 14, 19

Differences:

• 9 − 4 = 5
• 14 − 9 = 5
• 19 − 14 = 5

Again, every difference is the same.

Therefore, this is an arithmetic sequence.

Example 3

2, 4, 8, 16

Differences:

• 2
• 4
• 8

The differences are not equal.

Therefore, this is NOT an arithmetic sequence.

Characteristics of Arithmetic Sequences

An arithmetic sequence always has:

• A constant difference
• Predictable pattern
• Linear growth or decrease
• Equal spacing between numbers

If the difference changes, the sequence is not arithmetic.

Formula for the nth Term

The nth term formula is:

an=a1+(n−1)da_n = a_1 + (n-1)dan​=a1​+(n−1)d

Where:

• a₁ = first term
• d = common difference
• n = term number

Example:

Sequence:

3, 7, 11, 15…

Find the 10th term.

• First term = 3
• Difference = 4

Calculation:

10th term

= 3 + (10−1)×4

= 3 + 36

= 39

Real-Life Examples

Arithmetic sequences appear in many everyday situations.

A person saves $20 every week.

Savings:

• Week 1 = $20
• Week 2 = $40
• Week 3 = $60
• Week 4 = $80

This forms an arithmetic sequence because the increase is always $20.

Another example is climbing stairs where each floor contains the same number of steps.

Common Mistakes Students Make

Many students confuse arithmetic sequences with geometric sequences.

Arithmetic:

5, 10, 15, 20

Difference = 5

Geometric:

5, 10, 20, 40

Ratio = 2

Always check whether you are adding or subtracting the same number rather than multiplying or dividing.

Practice Questions

Question 1

Which sequence is arithmetic?

A.

2, 4, 6, 8

B.

3, 6, 12, 24

C.

5, 9, 16, 25

Answer:

A because every term increases by 2.

Question 2

Find the common difference.

Sequence:

11, 16, 21, 26

Answer:

5

Question 3

Find the next number.

100, 90, 80, 70

Answer:

60

Question 4

Is this arithmetic?

7, 10, 13, 16, 19

Answer:

Yes.

Common difference = 3.

Why Students Search This on Brainly

Many students search “Which of the following is an arithmetic sequence Brainly” because homework assignments often provide several number sequences and ask students to choose the arithmetic one. Instead of relying only on a posted answer, understanding the rule of equal differences allows you to solve similar questions independently and with confidence.

Conclusion

Arithmetic sequences are among the simplest and most important mathematical patterns. The key to identifyingwhich of the following is an arithmetic sequence brainly one is checking whether the difference between consecutive numbers remains constant throughout the sequence. Once you understand the concept of the common difference and know how to apply the nth-term formula, solving arithmetic sequence problems becomes straightforward. Whether you are preparing for a classroom test, completing homework, or searching for a Brainly-style explanation, mastering arithmetic sequences will strengthen your overall mathematical reasoning and make future sequence problems much easier to solve.

Frequently Asked Questions (FAQ)

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is always the same.

How do I know if a sequence is arithmetic?

Subtract each term from the next. If every difference is equal, the sequence is arithmetic.

What is the common difference?

The common difference is the constant amount added or subtracted between consecutive terms.

What is the arithmetic sequence formula?

The nth-term formula is:

an=a1+(n−1)da_n = a_1 + (n-1)dan​=a1​+(n−1)d

where a1a_1a1​ is the first term and $d$ is the common difference.

What is the difference between arithmetic and geometric sequences?

An arithmetic sequence changes by adding or subtracting the same number each time, while a geometric sequence changes by multiplying or dividing by the same number each time.

Why is this topic popular on Brainly?

Students frequently search for “which of the following is an arithmetic sequence brainly” to get help with homework, quizzes, and exam preparation, making it a common educational search query.