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Quizzes > High School Quizzes > Mathematics

Arithmetic Sequence Practice Quiz

Boost your confidence identifying arithmetic sequences today

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art depicting a trivia quiz on arithmetic sequences for high school students.

Which of the following sequences is arithmetic?
5, 10, 15, 22
4, 9, 14, 20
1, 3, 7, 9
2, 5, 8, 11
An arithmetic sequence has a constant difference between consecutive terms. In the sequence '2, 5, 8, 11', the difference is consistently 3.
What is the common difference of the arithmetic sequence: 7, 10, 13, 16?
4
2
5
3
The common difference is found by subtracting the first term from the second term (10 - 7 = 3). This difference remains the same throughout the sequence.
In an arithmetic sequence, the constant amount added to each term to get the next term is called:
Common Ratio
Common Difference
Constant Product
Arithmetic Mean
The term 'common difference' is used to describe the fixed amount added to each term in an arithmetic sequence. This distinguishes arithmetic sequences from geometric sequences, which use a common ratio.
Given the arithmetic sequence: -2, 1, 4, 7, ... which statement is true?
The sequence does not have a pattern
Each term decreases by 3
Each term is multiplied by -3
Each term increases by 3
Subtracting consecutive terms (-2 to 1, 1 to 4, 4 to 7) always gives a difference of 3. This consistent increase confirms the sequence is arithmetic.
Which of the following is NOT a property of arithmetic sequences?
They have a common difference
The ratio between consecutive terms is constant
Their terms form a linear pattern
They can be defined by an explicit formula
Arithmetic sequences are defined by a constant difference, not a constant ratio. A constant ratio is a property of geometric sequences, making this option the correct choice.
Find the 8th term of the arithmetic sequence: 3, 7, 11, ...
32
31
33
30
Using the formula a_n = a1 + (n-1)*d with a1 = 3 and d = 4, the 8th term is calculated as 3 + 7*4 = 31. This confirms that the sequence correctly follows an arithmetic progression.
Determine the 6th term of the arithmetic sequence with first term 2 and common difference 5.
30
25
27
32
By applying the formula a_n = a1 + (n-1)*d, we find a6 = 2 + 5*(6-1) = 27. This demonstrates the correct use of the arithmetic sequence formula.
Which equation represents the nth term of an arithmetic sequence with first term a1 and common difference d?
a_n = a1 + d*(n - 1)
a_n = a1 * d^(n - 1)
a_n = a1 + d*n
a_n = a1 * n + d
The correct formula for the nth term of an arithmetic sequence is a_n = a1 + d*(n - 1), which fully represents the additive nature of the sequence. The other options represent formulas for different types of sequences or are incorrectly formulated.
If an arithmetic sequence has a first term of 10 and a 10th term of 55, what is its common difference?
4
7
5
6
The 10th term is given by the equation 10 + 9d = 55. Solving for d gives 9d = 45, so d = 5, which is the constant amount added at each step.
Which of the following sequences is arithmetic?
5, 10, 15, 30, 45
2, 4, 8, 16, 32
1, 4, 9, 16, 25
12, 9, 6, 3, 0
An arithmetic sequence has a constant difference between terms. In the sequence '12, 9, 6, 3, 0', the difference is consistently -3, confirming its arithmetic nature.
Find the missing number in the arithmetic sequence: 7, ___, 13, 16.
10
12
11
9
Let the missing term be x. Setting up the equation x - 7 = 13 - x gives 2x = 20, so x = 10. This value maintains the constant difference required in an arithmetic sequence.
If an arithmetic sequence has a common difference of 4 and the 7th term is 31, what is the first term?
8
7
10
9
Using the formula a7 = a1 + 6*4 = 31, we solve for a1, yielding a1 = 31 - 24 = 7. This confirms the starting value of the sequence.
Which expression best represents the sum of the first n terms of an arithmetic sequence with initial term a1 and common difference d?
S = n[a1 + (n-1)d]
S = (n/2)[2a1 + (n-1)d]
S = (n/2)[a1 + (n-1)d]
S = a1 * n + d
The sum of the first n terms of an arithmetic sequence is given by S_n = (n/2)[2a1 + (n-1)d]. This formula properly accounts for both the initial term and the resulting increase over n terms.
What is the 15th term of the arithmetic sequence: 4, 9, 14, ...?
74
70
75
69
Using the nth term formula, a15 = 4 + (15-1)*5 = 4 + 70 = 74. This calculation confirms the value of the 15th term in the sequence.
If the 3rd term of an arithmetic sequence is 12 and the 7th term is 28, what is the common difference?
2
6
8
4
By writing the equations a1 + 2d = 12 and a1 + 6d = 28, subtracting them gives 4d = 16. Solving this yields d = 4, which is the constant increment in the sequence.
An arithmetic sequence has the property that the sum of its first n terms is given by 3n² + 2n. What is the common difference of the sequence?
5
6
7
4
The nth term of a sequence can be found by subtracting S(n-1) from S(n). Doing so leads to a_n = 6n - 1, which shows that the difference between consecutive terms is 6.
If the 50th term of an arithmetic sequence is 147 and the common difference is 3, what is the first term?
3
0
5
1
Using the formula a50 = a1 + 49*3 and substituting a50 = 147, we solve for a1 = 147 - 147 = 0. This confirms that the first term of the sequence is 0.
The first term of an arithmetic sequence is unknown. If the sum of the first 20 terms is 410 and the common difference is 3, determine the first term.
8
-7
7
-8
Using the sum formula S_n = (n/2)[2a1 + (n-1)d] with n = 20 and d = 3, we set up the equation 10*(2a1 + 57) = 410. Solving for a1 gives 2a1 + 57 = 41, so a1 = -8.
In an arithmetic sequence, if the 8th term is 29 and the 12th term is 45, find the sum of the first 15 terms.
420
465
450
435
First, determine the common difference: d = (45 - 29) / (12 - 8) = 4. Then, using a8 = a1 + 7d = 29, we find a1 = 1. Finally, applying the sum formula S15 = (15/2)[2*1 + 14*4] results in a sum of 435.
An arithmetic sequence has three consecutive terms such that the sum of the middle term and the last term is 24. If the common difference is 4, what is the first term?
4
8
10
6
Represent the three consecutive terms as a, a+4, and a+8. The condition (a+4) + (a+8) = 24 leads to 2a + 12 = 24, so a = 6. This is the first term of the sequence.
0
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Study Outcomes

  1. Identify arithmetic sequences among various numerical sequences.
  2. Determine the common difference of a given arithmetic sequence.
  3. Apply arithmetic sequence rules to solve sequence problems.
  4. Analyze patterns in sequences to confirm arithmetic progression.
  5. Synthesize information from sequence problems to justify reasoning.

Arithmetic Sequence Cheat Sheet

  1. Understanding Arithmetic Sequences - Arithmetic sequences are like number staircases where each step changes by the same fixed amount. Recognizing this steady pattern helps you quickly predict future terms and beat sequence puzzles in no time! GeeksforGeeks: Arithmetic Sequence Formula
  2. Identifying the Common Difference - Finding the magic number that connects each term is simple: subtract any term from its next neighbor. That result is your common difference, the secret sauce of arithmetic sequences, unlocking all further terms with just one calculation. GeeksforGeeks: Identifying Common Difference
  3. Formula for the nth Term - With the formula aₙ = a₝ + (n - 1) × d, you have a roadmap to any term in the sequence. This shortcut means you don't have to list every term - just plug in your values and watch the sequence unfold mathematically! GeeksforGeeks: nth Term Formula
  4. Calculating the Sum of Terms - Summing up the first n terms is a breeze with Sₙ = n/2 × (2a₝ + (n - 1) × d). Whether you're adding up your weekly allowances or puzzle sequence sums, this formula keeps your calculations lightning-fast! GeeksforGeeks: Sum of Terms
  5. Recognizing Arithmetic Sequences - Not every list is arithmetic, so check each neighboring pair: if their differences match, you've struck gold. Once that constant gap is confirmed, you're officially an arithmetic-sequence detective! GeeksforGeeks: Recognizing Arithmetic Sequences
  6. Real-World Applications - From planning your monthly savings to modeling linear growth in science experiments, arithmetic sequences pop up everywhere. Understanding how to spin up these sequences helps you solve practical problems and ace real-life math challenges! It's like translating everyday scenarios into math's universal language! GeeksforGeeks: Real-World Uses
  7. Graphing Arithmetic Sequences - Plot an arithmetic sequence on a graph, and voila - a straight line appears! This visual cue reveals the constant rate of change and makes spotting patterns super easy. Math is Fun: Graphing Arithmetic Sequences
  8. Finding the Number of Terms - Want to know how many steps it takes to reach a specific term? Rearrange the nth-term formula to n = ((aₙ - a₝)/d) + 1, and you'll nail the count in one go. No more tedious listing - just clever algebra! GeeksforGeeks: Number of Terms
  9. Arithmetic Mean - Aspire to find the middle term between two numbers? The arithmetic mean is your go-to: simply add them and divide by two. In terms of sequences, it's the secret middle friend that keeps the pattern balanced! GeeksforGeeks: Arithmetic Mean
  10. Common Difference Significance - If the common difference is positive, your sequence is on the upswing; if it's negative, you're sliding down. Grasping this sign switch gives you instant insight into whether a sequence is climbing, falling - or even staying put if d = 0! GeeksforGeeks: Difference Significance
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