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Arithmetic Progressions Quiz - CBSE Class 10 Mathematics

Free practice quiz: Arithmetic Progressions (CBSE Class 10 Mathematics). 16 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 10 Mathematics practice quiz has 16 multiple-choice questions on Arithmetic Progressions, and 16 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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About this topic

An AP is a sequence in which every term is got by adding a fixed number d to the previous term. Knowing the first term a and common difference d lets you find any term and the sum of any number of terms.

AP: a, a + d, a + 2d, a + 3d, … where a = first term, d = common difference.
d = a_(n + 1) − a_n. Same value for every pair of consecutive terms.
d > 0: AP increases. d < 0: AP decreases. d = 0: all terms equal.
Finite AP has a last term l. Infinite AP never ends.
Three numbers a, b, c are in AP if 2b = a + c.
a_n = S_n − S_(n − 1) for n ≥ 2. Also a₁ = S₁.
To show a list is an AP, check that all consecutive differences are equal.

Learn the key ideas Beta

What an AP is

An AP is a list of numbers where you add the same number each time.
That fixed number is the common difference d.
d can be positive, negative or zero.

Common difference

\[d = a_{2} - a_{1} = a_{n+1} - a_{n}\]

Common mistake: Finding d as earlier term minus later term. Always do later term minus earlier term.

The nth term

a is the first term and n is the position of the term.
To reach term n, you add d only (n − 1) times.

nth term

\[a_{n} = a + (n-1)d\]

nth term from the end (last term l)

\[l - (n-1)d\]

Common mistake: Writing a + nd. The first term already counts as term 1, so use (n − 1).

Sum of the first n terms

Pair the first and last terms; each pair has the same sum.
Use the second formula when you know the last term l.

Sum using d

\[S_{n} = \frac{n}{2}\left[2a + (n-1)d\right]\]

Sum using last term

\[S_{n} = \frac{n}{2}(a + l)\]

A term from sums

\[a_{n} = S_{n} - S_{n-1}\]

Common mistake: Forgetting the n/2 at the front, or using n where the formula needs (n − 1).

Three terms in an AP

If a, b, c are in AP, then b is the middle (average) term.
For three unknown terms in AP, take a − d, a, a + d.

Middle term

\[2b = a + c\]

Common mistake: Choosing a, a + d, a + 2d for a sum problem. The symmetric choice cancels d.

Exam tips

Check d with two different pairs of terms before you use it.
The number of terms n must be a positive whole number.
Sum of the first n natural numbers is n(n + 1)/2.

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

What is the common difference in the sequence: 3, 6, 9, 12, ...?
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Answer: C. 3
The sequence is an arithmetic progression where each term increases by 3. Therefore, the common difference is 3.
What is the 6th term of the arithmetic sequence: 4, 9, 14, 19?
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Answer: A. 29
The common difference is 5. The 6th term is calculated as 4 + 5*5 = 29.
Determine the 12th term of the sequence: 15, 10, 5, 0, ...
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Answer: A. -45
Common difference is -5. The 12th term is 15 + 11*(-5) = -45.
A sequence has a3 = 19 and a7 = 47. What is the common difference?
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Answer: A. 7
The difference in terms is (47 - 19) / (7 - 3) = 7.
The sum of the first 15 terms of an AP is 525, and the first term is 10. Find the common difference.
Show answer
Answer: A. 2
Using the formula S_n = n/2 * (2a + (n-1)d) and solving for d, we get d = 2.

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