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Sequences and Series Practice Questions

JEE · Mathematics · 1639 free MCQs with instant results and detailed explanations.

1639
Total
350
Easy
668
Medium
621
Hard

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Topics in Sequences and Series

AP 190
GP 208
HP 198
AGP 175
Sum of n Terms 151
Special Series 254
Method of Differences 130
Telescoping 333

Sample Questions from Sequences and Series

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
What is the sum of the first 10 terms of the AP 2, 5, 8, ...?
A. 165
B. 150
C. 170
D. 180
Show Answer & Explanation
Correct Answer: A
Using the sum formula S_n = n/2 * (2a + (n-1)d). Here, a = 2, d = 3, n = 10.
Q2
Easy
What is the 10th term of the AP if the first term is 2 and the common difference is 7?
A. 69
B. 60
C. 70
D. 65
Show Answer & Explanation
Correct Answer: C
Using the nth term formula for AP gives us the desired term.
Q3
Easy
What is the common ratio of the geometric series: 3, 6, 12, 24?
A. 2
B. 3
C. 4
D. 1.5
Show Answer & Explanation
Correct Answer: A
The common ratio (r) is found by dividing any term by the previous term. Here, r = 6/3 = 2.
Q4
Medium
If the first term of an AP is x and the common difference is y, express the 12th term in terms of x and y.
A. x + 11y
B. x + 12y
C. x + 10y
D. x + 9y
Show Answer & Explanation
Correct Answer: A
The nth term formula a_n = a + (n-1)d gives a_{12} = x + (12-1)y = x + 11y.
Q5
Medium
If the 4th term of an AP is 12 and the 7th term is 21, what is the common difference?
A. 3
B. 2
C. 1
D. 5
Show Answer & Explanation
Correct Answer: A
The common difference d can be found using the formula for the nth term and the two terms provided.
Q6
Medium
In an AP, if the first term is 'a' and the common difference is 'd', what will be the sum of the first n terms?
A. n/2 (2a + (n-1)d)
B. n (a + d)
C. n (2a + (n-1)d)
D. n^2 (a + d)
Show Answer & Explanation
Correct Answer: A
The sum of the first n terms of an AP is given by the formula S_n = n/2 (2a + (n-1)d).
Q7
Medium
If the 1st term of an AP is 10 and the last term is 46 with 10 terms, what is the common difference?
A. 4
B. 3.6
C. 5
D. 6
Show Answer & Explanation
Correct Answer: A
The last term can be expressed as a + (n-1)d = 46. Substitute a and n to find d.
Q8
Hard
In an AP, if the first term is a, the common difference is d, and the number of terms is n, what is the value of the 100th term?
A. a + 99d
B. a + 100d
C. a + 98d
D. a + 101d
Show Answer & Explanation
Correct Answer: A
The nth term of an AP is given by the formula a_n = a + (n-1)d. Thus for n=100, the formula simplifies to a + 99d.
Q9
Hard
In an arithmetic progression, if the first term is a and the last term is l, with n total terms, what is the formula for the sum of all terms?
A. n/2 * (a + l)
B. n(a + l)
C. n/2 * (2a + (n-1)d)
D. n/2 * (2a + n)
Show Answer & Explanation
Correct Answer: A
The sum of the terms in an AP can be calculated using the formula S_n = n/2 * (first term + last term).
Q10
Hard
If the first term of an AP is m and the common difference is k, express the 15th term in terms of m and k.
A. m + 14k
B. m + 15k
C. m + 13k
D. m + 12k
Show Answer & Explanation
Correct Answer: A
Using the nth term formula a_n = a + (n-1)d, the 15th term can be expressed as m + 14k.

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Sequences and Series — JEE Mathematics Practice Questions Online

This page contains 1639 practice MCQs for the chapter Sequences and Series in JEE Mathematics. The questions are organized by difficulty — 350 easy, 668 medium, 621 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 8 topics, giving you comprehensive coverage of the entire chapter.