Education
Which of the Following Is an Arithmetic Sequence Brainly? Complete Guide (2026)
If you have searched “which of the following is an arithmetic sequence Brainly,” you are probably trying to solve a homework question, prepare for a quiz, or understand the concept of arithmetic sequences more clearly. Thousands of students use educational websites to verify answers, but simply copying an answer rarely helps build a solid understanding of mathematics. The good news is that arithmetic sequences are among the easiest algebra concepts once you understand the underlying pattern. Every arithmetic sequence follows a predictable rule based on adding or subtracting the same number repeatedly, making it much easier to identify than many other number patterns.
In this comprehensive guide, you’ll learn exactly what an arithmetic sequence is, how to recognize one quickly, the formulas involved, common mistakes students make, and multiple solved examples similar to questions often found on homework help platforms. By the end of this article, you’ll be able to solve arithmetic sequence questions confidently without relying solely on answer-sharing websites.
What Is an Arithmetic Sequence?
An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is always the same. This constant difference is called the common difference, usually represented by the letter d. Unlike random number patterns, arithmetic sequences grow or decrease at a steady rate, making them one of the fundamental concepts in algebra and mathematics. Students encounter arithmetic sequences in school mathematics, standardized tests, and many real-world applications such as financial planning, engineering, computer programming, and data analysis.
For example:
- 2, 5, 8, 11, 14…
- 12, 9, 6, 3, 0…
- -4, 0, 4, 8, 12…
Each sequence changes by exactly the same amount every time, which is the defining characteristic of an arithmetic sequence.
How to Identify an Arithmetic Sequence
The easiest method is to subtract one term from the next.
For example:
Sequence:
10, 15, 20, 25, 30
Differences:
15−10 = 5
20−15 = 5
25−20 = 5
30−25 = 5
Since every difference equals 5, this is an arithmetic sequence.
Now consider:
2, 4, 8, 16, 32
Differences:
2
4
8
16
The differences are not constant, so this is not an arithmetic sequence.
Common Brainly-Style Questions
Example 1
Which of the following is an arithmetic sequence?
A. 3, 6, 9, 12, 15
B. 2, 4, 8, 16
C. 1, 1, 2, 3, 5
D. 5, 10, 20, 40
Answer:
Option A is correct because every number increases by 3.
Example 2
Find the common difference.
Sequence:
18, 25, 32, 39, 46
Subtract:
25−18 = 7
32−25 = 7
39−32 = 7
46−39 = 7
Therefore,
Common Difference = 7
Example 3
Is this an arithmetic sequence?
100, 95, 90, 85, 80
Yes.
Each term decreases by 5.
Arithmetic Sequence Formula
The nth term formula is:
aₙ = a₁ + (n − 1)d
Where:
- a₁ = first term
- d = common difference
- n = term number
- aₙ = nth term
This formula allows you to find any term without listing all previous terms.
Step-by-Step Example
Find the 20th term.
Sequence:
5, 9, 13, 17…
First term = 5
Difference = 4
n = 20
Formula:
a₂₀ = 5 + (20−1) × 4
= 5 + 76
= 81
Therefore, the twentieth term equals 81.
Real-Life Applications
Arithmetic sequences are not limited to classroom exercises. They are widely used in budgeting, salary progression, installment plans, inventory management, scheduling, construction measurements, computer algorithms, and scientific modeling. Any situation involving equal increases or decreases over time can often be represented using an arithmetic sequence, making the concept valuable far beyond mathematics exams.
Common Mistakes Students Make
Many learners confuse arithmetic sequences with geometric sequences, assuming any increasing pattern qualifies as arithmetic. However, arithmetic sequences rely on a constant difference, while geometric sequences rely on a constant ratio. Another common mistake is checking only the first two numbers instead of verifying the difference between every consecutive pair. Students may also substitute incorrect values into the nth-term formula or forget that decreasing sequences can still be arithmetic if the common difference is consistently negative. Carefully checking each step helps avoid these errors.
Practice Questions
- Which sequence is arithmetic?
A. 4, 8, 12, 16
B. 3, 6, 12, 24
C. 1, 2, 4, 8
D. 5, 25, 125
Answer: A
- Find the common difference.
9, 13, 17, 21
Answer:
Difference = 4
- Is this arithmetic?
40, 34, 28, 22
Answer:
Yes
Difference = −6
Tips for Solving Arithmetic Sequence Questions Faster
Always begin by calculating the difference between consecutive terms. If every difference is identical, you have an arithmetic sequence. When finding a specific term, use the nth-term formula instead of writing out every term, especially for large values of n. Double-check your arithmetic, pay attention to negative differences, and practice with a variety of examples to build speed and accuracy.
Conclusion
Understanding arithmetic sequences becomes straightforward once you recognize the importance of a constant common difference. Instead of memorizing answers from homework forums, focus on the simple process of checking the difference between consecutive numbers and applying the nth-term formula when needed. With consistent practice, you will be able to solve questions like “Which of the following is an arithmetic sequence?” quickly and confidently, whether they appear in homework, classroom tests, or competitive exams. Mastering this topic also provides a strong foundation for more advanced mathematical concepts involving patterns, series, and algebraic reasoning.
Frequently Asked Questions (FAQ)
What is an arithmetic sequence?
An arithmetic sequence is a list of numbers in which the difference between consecutive terms remains constant.
How do I know if a sequence is arithmetic?
Subtract each term from the next. If every difference is the same, it is an arithmetic sequence.
What is the common difference?
The common difference is the fixed value added to or subtracted from each term to obtain the next term.
What is the formula for the nth term?
The nth term is calculated using the formula:
aₙ = a₁ + (n − 1)d
where a₁ is the first term and d is the common difference.
Can an arithmetic sequence decrease?
Yes. If the common difference is negative, the sequence decreases while still remaining arithmetic.
What is the difference between an arithmetic and a geometric sequence?
An arithmetic sequence changes by adding or subtracting the same amount each time, while a geometric sequence changes by multiplying or dividing by the same ratio.