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Quizzes > High School Quizzes > Mathematics

Arithmetic Series Practice Quiz

Master series skills with real-life applications now

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Paper art representing a trivia quiz on high school arithmetic series mastery.

What defines an arithmetic sequence?
A series that alternates between addition and subtraction.
A list of numbers with a constant difference between consecutive terms.
A randomly generated list of numbers with no predictable pattern.
A sequence where each term is obtained by multiplying the previous term by a constant factor.
An arithmetic sequence is characterized by a constant difference between successive terms. This consistency distinguishes it from geometric or random sequences.
Which formula represents the n-th term (aₙ) of an arithmetic sequence?
n²(a + d)
a*n + d
(a + d)❿
a + (n-1)d
The correct formula for the n-th term of an arithmetic sequence is aₙ = a + (n-1)d. This shows that each new term increases by a constant d.
What is the correct formula for the sum of the first n terms of an arithmetic series?
Sₙ = a + (n-1)d
Sₙ = n/2 * [2a + (n-1)d]
Sₙ = (a + (n-1)d)/2
Sₙ = n(a + d)
The sum of an arithmetic series is calculated with Sₙ = n/2 * [2a + (n-1)d]. This formula effectively pairs the first and last terms to find the aggregate sum.
If an arithmetic sequence starts with 3 and has a common difference of 4, what is the 5th term?
18
19
15
23
Using the formula aₙ = a + (n-1)d, the 5th term is computed as 3 + 4 - (5-1) = 19. This demonstrates the step-by-step process of arithmetic progression.
What is the common difference in the arithmetic sequence: 10, 15, 20, 25, ... ?
4
20
5
10
Subtracting consecutive terms (15 - 10) gives the common difference of 5. This constant increment confirms the sequence's arithmetic nature.
Find the sum of the first 8 terms of the arithmetic sequence: 2, 5, 8, ...
100
88
90
96
Using the sum formula Sₙ = n/2 * [2a + (n-1)d] with a = 2, d = 3, and n = 8, we calculate S₈ = 8/2 - (4 + 21) = 4 - 25 = 100. This approach reinforces the technique for summing an arithmetic series.
Determine the 10th term of an arithmetic sequence with a first term of 7 and a common difference of 3.
40
31
34
37
The nth term is found using aₙ = a + (n-1)d. Substituting a = 7, d = 3, and n = 10 gives 7 + 9 - 3 = 34. This process underscores the regularity of term increments.
If the first term of an arithmetic sequence is 4 and the 20th term is 43, what is the sum of the first 20 terms?
460
500
470
480
The sum is computed via Sₙ = n/2 - (first term + last term). For n = 20, S₂₀ = 20/2 - (4 + 43) equals 10 - 47, which is 470. This highlights the practical utility of the sum formula.
Find the common difference of the arithmetic sequence: 3, 7, 11, ... if the 15th term is 59.
3
5
6
4
The 15th term a₝₅ is given by a + 14d. With a = 3 and a₝₅ = 59, the equation 3 + 14d = 59 simplifies to 14d = 56, leading to d = 4. This problem reinforces solving for d using a given term.
In an arithmetic series, if the sum of the first 10 terms is 155 and the first term is 2, what is the common difference?
4
2
5
3
By applying the formula Sₙ = n/2 [2a + (n-1)d], we set up 10/2 - [4 + 9d] = 155. Solving 5 - (4 + 9d) = 155 leads to 4 + 9d = 31, so d = 3. This question practices isolating d from the sum formula.
Find the missing term in the arithmetic sequence: 8, __, 14, 17.
12
11
13
10
Assuming a constant difference, use the given terms: the third term equals 8 + 2d = 14, which gives d = 3. The missing second term is then 8 + 3 = 11. This reinforces the method of finding missing values in an arithmetic sequence.
For the arithmetic sequence 1, 4, 7, 10, ..., for what value of n does the series sum equal 70?
7
10
8
6
The sum formula Sₙ = n/2 - (3n - 1) is used here. Testing n = 7 yields S₇ = 7/2 - (21 - 1) = 7/2 - 20 = 70, which satisfies the condition.
An arithmetic sequence has its third term as 12 and its seventh term as 24. What is the first term?
6
9
7
8
Setting up the equations a + 2d = 12 and a + 6d = 24, subtracting them gives 4d = 12, so d = 3. Substituting back, a = 12 - 2 - 3 = 6. This confirms the method of using term differences to find unknowns.
If the common difference of an arithmetic sequence is negative, what is a true statement about the sequence?
The series is decreasing, with each term smaller than the previous term.
The series is increasing, with each term larger than the previous term.
The sequence will have alternating positive and negative terms.
The first term must be negative.
A negative common difference means that every subsequent term is less than the one before, leading to a decreasing sequence. The sign of the first term is independent of the common difference.
Simplify the sum formula Sₙ = n/2*(2a + (n-1)d) when a = 3 and d = 5.
n(5n+1)/2
n(5n)/2
n(5n+5)/2
n(5n-1)/2
Substituting a = 3 and d = 5 into the formula gives Sₙ = n/2*(6 + 5n - 5) which simplifies to n/2*(5n + 1). This question emphasizes algebraic simplification.
For an arithmetic sequence, if the 4th term is 11 and the 15th term is 32, what are the first term and common difference?
First term = 58/11, Common difference = 11/21
First term = 21/11, Common difference = 58/11
First term = 58/11, Common difference = 21/11
First term = 11, Common difference = 2
Using the equations a + 3d = 11 and a + 14d = 32, subtracting yields 11d = 21, so d = 21/11. Substituting back gives a = 11 - 3 - (21/11) = 58/11. This problem requires solving a system of linear equations involving fractions.
Let Sₙ be the sum of the first n terms given by Sₙ = 3n² + 2n. Find the 8th term of the arithmetic series.
46
47
45
48
The nth term is found by subtracting consecutive sums: a₈ = S₈ - S₇. Calculating S₈ = 208 and S₇ = 161, we find a₈ = 47. This method highlights the strategy of deriving terms from cumulative sums.
Given the sum formula Sₙ = n(4 + 3n)/2 for an arithmetic series, determine the first term and the common difference.
First term = 4, Common difference = 3
First term = 7/2, Common difference = 3
First term = 7/2, Common difference = 4
First term = 7, Common difference = 3
The first term is obtained from S₝ which is (4+3)/2 = 7/2. Then, computing a₂ as S₂ - S₝ shows that the common difference is 3. This problem tests the ability to reverse-engineer parameters from a sum formula.
An arithmetic sequence is defined by the formula aₙ = 2n + 3. Is this sequence arithmetic, and if so, what are its first term and common difference?
Arithmetic; First term = 5, Common difference = 3
Not arithmetic
Arithmetic; First term = 5, Common difference = 2
Arithmetic; First term = 3, Common difference = 2
Since aₙ = 2n + 3 is a linear function, the difference between successive terms is constant (a₂ - a₝ = 2). The first term, a₝, is 2(1) + 3 = 5, confirming that the sequence is arithmetic with a common difference of 2.
Consider an arithmetic series with sum Sₙ = n² + 6n. Find the 4th term of the sequence.
15
13
12
14
To determine the 4th term, subtract the sum of the first 3 terms from the sum of the first 4 terms: a₄ = S₄ - S₃. With S₄ = 40 and S₃ = 27, we find a₄ = 13. This approach illustrates the extraction of a single term from a cumulative sum formula.
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Study Outcomes

  1. Understand the definition and components of an arithmetic series.
  2. Apply the formula for the sum of an arithmetic series to solve problems.
  3. Analyze sequences to identify common differences and first terms.
  4. Solve real-world problems by constructing and evaluating arithmetic series.

4.05 Arithmetic Series & Applications Cheat Sheet

  1. Understanding Arithmetic Sequences - Arithmetic sequences are like climbing a staircase where you step by the same height each time, for example 2, 5, 8, 11 with a step of 3. Spotting this constant difference is your secret weapon for tackling sequence problems with confidence. Math is Fun: Arithmetic Sequences
  2. Formula for the nth Term - The magic formula an = a1 + (n − 1)d lets you jump straight to any term in the sequence like a pro. No need to list every number - just plug in the values and watch the answer appear! OpenStax: nth Term Formula
  3. Calculating the Sum of Terms - Want to add up the first n terms without writing them all down? Use Sn = n/2 [2a1 + (n − 1)d] to calculate sums in a flash. It's like having a shortcut to the finish line! OpenStax: Sum Formula
  4. Identifying the Common Difference - The secret sauce d is found by subtracting any term from the next: d = an − an‑1. Consistency means you have an arithmetic sequence, and you're ready to roll. Online M. School: Common Difference
  5. Recognizing Arithmetic Series - An arithmetic series is just the sum of terms in an arithmetic sequence. Think of it as gathering all the staircase steps into one big stack! Wolfram MathWorld: Arithmetic Series
  6. Sum Formula with the Last Term - If you know the last term an, you can simplify Sn = n/2 (a1 + an) to get the total in just two numbers. It's perfect when the final step is already given. OpenStax: Alternate Sum Formula
  7. Real-World Applications - Arithmetic sequences pop up in savings plans, where you deposit the same amount each period, or in pattern designs. Spotting these real life examples makes math a lot more exciting! Cuemath: Applications of Arithmetic Sequences
  8. Deriving the Sum Formula - Pairing the first and last terms (a1 + an), the second and second‑last, and so on, reveals the pattern Sn = n/2 (a1 + an). Understanding this creative derivation boosts your confidence and retention. Math is Fun: Sum Formula Derivation
  9. Sequences vs Series - A sequence is an ordered list of numbers, while a series is the sum of those numbers - like the difference between steps and the total height you climb. Mastering this distinction is crucial for acing exams. Online Math Learning: Sequences vs Series
  10. Practice with Examples - Flex your math muscles by solving plenty of arithmetic sequence and series challenges, from basic to tricky. The more you practice, the more these patterns become second nature! OpenOmnia: Practice Exercises
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