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Quizzes > Mathematics > Algebra

How Well Do You Know Arithmetic Progression? Start the Quiz!

Put Your Arithmetic Sequence Skills to the Test

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art featuring folded numbers and geometric shapes forming arithmetic progression sequence on golden yellow background

Are you ready to push your limits and master arithmetic sequences? Our free arithmetic progression quiz is designed to challenge your understanding of AP formula practice and turn those tricky progression questions into easy wins. Whether you're brushing up on fundamentals or aiming for top scores, this arithmetic sequence quiz will test your problem-solving skills and boost confidence. Explore our problems on arithmetic progression to sharpen your approach, then dive into advanced arithmetic and geometric sequences practice to see how you stack up. Jump in now - tackle this math progression test and track your progress every step of the way!

Easy
What defines an arithmetic progression (AP)?
A sequence where each term is multiplied by a constant factor
A sequence where the difference between consecutive terms is constant
A sequence where each term is the square of its index
A sequence with only positive terms
An arithmetic progression is defined by having a fixed constant difference between successive terms. This constant difference is often denoted by d. If you subtract any term from the next, you'll always get the same value d in an AP. For more details, see Arithmetic progression on Wikipedia.
If the first term of an AP is 3 and the common difference is 4, what is the fifth term?
19
18
15
11
The nth term of an AP is a_n = a_1 + (n-1)d. Here, a_1 = 3, d = 4, and n = 5 so a_5 = 3 + 4×4 = 19. You can learn more at Math is Fun: Sequences and Series.
What is the sum of the first 10 terms of an AP with first term 1 and common difference 2?
100
110
95
90
The sum formula is S_n = n/2 [2a_1 + (n?1)d]. For n=10, a_1=1, d=2, so S_10 = 10/2 [2+ (9×2)] =5×20 =100. See more at Khan Academy: Sequences.
If the fourth term of an AP is 10 and the common difference is 3, what is the first term?
1
10
13
-2
We use a_4 = a_1 + 3d, so 10 = a_1 + 3×3 ? a_1 = 10 ?9 = 1. This demonstrates solving backwards using the nth term formula. For further reading, see nth term of an AP.
Medium
In the sequence 7, x, 3 forming an AP, what is x?
5
-5
4
6
In an AP the difference between consecutive terms is equal: x?7 = 3?x ? 2x = 10 ? x = 5. This enforces the constant difference property. See Arithmetic sequences at Math is Fun.
What is the sum of the AP: 5, 8, 11, …, 50?
440
435
450
400
First find n: 5 + (n?1)·3 = 50 ? n = 16. Then S_n = n/2(a_1 + a_n) = 16/2 (5+50) =8×55 =440. More at Sum of an AP.
Which of these expressions is the standard formula for the sum of the first n terms of an AP with first term a and common difference d?
n/2 [2a + (n?1)d]
(n+1)/2 [2a + (n?1)d]
(n?1)/2 [2a + (n+1)d]
n [a + (n?1)d]
The standard sum formula for an AP is S_n = n/2 [2a + (n?1)d]. It derives from pairing terms from ends inward. For a deeper proof, refer to Arithmetic progression sum.
Which formula gives the nth term of an AP with first term a? and common difference d?
a? = a? + (n?1)d
a? = a? + nd
a? = (a? + d)?
a? = a?·d??¹
By definition, each term increases by d: a? = a? + (n?1)d. Alternatives represent geometric or other sequences. Learn more at Khan Academy Sequences.
Hard
If the 10th term of an AP is 32 and the 20th term is 72, what is the common difference?
4
5
3
6
We have a + 9d = 32 and a + 19d = 72. Subtracting gives 10d = 40 ? d = 4. This is a system of linear equations for AP terms. See Arithmetic progression.
For an AP where the sum of the first n terms is S? = 3n² + 5n, what is the explicit formula for the nth term a??
6n + 2
3n + 5
6n ? 2
3n² + 5
The nth term is a? = S? ? S??? = [3n²+5n] ? [3(n?1)²+5(n?1)] = 6n + 2. This uses telescoping of sums. More details at BBC Bitesize: Sequences.
How many terms are in the AP 18, 15, 12, …, ?12?
11
10
12
9
General term: 18 + (n?1)(-3) = ?12 ? (n?1) = 10 ? n = 11. Thus there are 11 terms. For this method, see nth term of an AP.
Expert
In an AP, the sum of the first 5 terms is 25 and the sum of terms 6 to 10 is 65. What is the common difference?
8/5
2
5/2
4
S? = 25 and S?? = S? + 65 = 90. Using S? = n/2(2a + (n?1)d): 90 = 5(2a + 9d) and 25 = 5/2(2a + 4d). Solving gives d = 8/5. See Sum formula details.
0
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Study Outcomes

  1. Understand AP Fundamentals -

    Grasp the basic structure of an arithmetic progression, including the roles of the first term and the common difference, as introduced in this quiz challenge.

  2. Calculate Individual Terms -

    Apply the nth-term formula to determine any term in an arithmetic sequence quickly and accurately during your AP formula practice.

  3. Compute Sequence Sums -

    Use the sum formula for arithmetic progressions to find the total of a series of terms, reinforcing your progression questions skills.

  4. Analyze Sequence Patterns -

    Identify and verify arithmetic sequences by examining term-to-term differences in our arithmetic sequence quiz format.

  5. Apply AP Formulas in Context -

    Solve real-world and theoretical problems by selecting and using the appropriate arithmetic progression formulas in this free math progression test.

Cheat Sheet

  1. Understanding the Basics of an Arithmetic Progression -

    Arithmetic progressions (APs) are sequences with a constant difference between consecutive terms, called the common difference d. Identifying whether a sequence like 5, 8, 11, … is an AP hinges on checking that each term increases by the same amount (here d=3). Keep an eye out for this simple rule to quickly spot APs in quizzes and study materials (source: Khan Academy).

  2. Formula for the nth Term -

    In an AP, the nth term is given by a_n = a_1 + (n - 1)d, where a_1 is the first term and d is the common difference. For example, if a_1=2 and d=5, then a_10 = 2 + 9×5 = 47, making it easy to jump straight to any position (MIT OpenCourseWare). Practice this formula to become lightning-fast at finding terms.

  3. Sum of the First n Terms -

    The sum formula S_n = n/2 (a_1 + a_n) or S_n = n/2 [2a_1 + (n - 1)d] lets you calculate totals without adding each term individually. For instance, summing the first 20 terms of 3, 7, 11, … uses S_20 = 20/2 [2×3 + 19×4] = 10×82 = 820 (University of Cambridge). A handy mnemonic is "half n times endpoints or double-start plus jumps" to recall both versions.

  4. Finding the Common Difference -

    Determining d is as easy as subtracting any term from its successor: d = a_{n+1} - a_n. If you see 15, 12, 9, … then d = 12 - 15 = - 3, revealing a descending AP (MIT OpenCourseWare). This simple subtraction trick makes solving progression questions a breeze and keeps you on track under timed quiz conditions.

  5. Solving for Unknown Terms -

    When an AP problem gives two nonconsecutive terms, set up equations using a_n = a_1 + (n - 1)d to find a_1 and d. For example, if the 5th term is 20 and the 12th term is 50, then 20 = a_1 + 4d and 50 = a_1 + 11d, so subtract to get d = 30/7 before solving for a_1 (University of Oxford Math). Systematic equation work like this will have you breezing through progression questions in no time!

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