Sequences

Change Setup
๐Ÿ“˜ Comprehensive Syllabus & Examination Guide

Sequences

Official curriculum roadmap, subject/topic distribution, negative marking rules, pacing guidelines, and solved sample questions.

๐ŸŽฏ Mapped Subjects & Topic Question Distribution

Total Question Pool 100%
10 MCQs
Combined Active Syllabus
Sequences
10 MCQs
Topic Pool
๐Ÿ“Š Question Pool Structure
10 MCQs across fundamental, intermediate, and advanced concept tiers.
โšก Recommended Pacing
45 to 60 seconds per MCQ. Flag complex problems and preserve 10 minutes for final revision.
โš–๏ธ Scoring & Negative Marking
+1 mark per correct answer. In competitive tests with negative marking, -0.25 applies for incorrect guesses.

๐Ÿ’ก Strategic Preparation & Exam Hall Guidelines

To maximize your score on Sequences, candidates are advised to follow a structured three-pass approach. In the First Pass, solve all direct recall and formula-based questions within 30 seconds each to secure foundational marks. In the Second Pass, tackle multi-step analytical and quantitative reasoning problems. In the Third Pass, review marked questions and verify calculations.

Practice with the interactive player below to evaluate your speed and accuracy under real exam pressure. Every question features full mathematical formulas, step-by-step worked solutions, and conceptual explanations vetted by Apex Rankers Academy subject matter specialists.

Ready to test your knowledge? Launch interactive 1-by-1 practice with instant feedback, bookmarking, and step-by-step rationales.
Solved Blueprint Examples

๐Ÿ“ Pre-Rendered Solved Sample Questions & Detailed Solutions

Showing 10 solved representative questions

Review the solved problems below to understand question phrasing, answer choices, and step-by-step solution logic prior to starting the full interactive practice drill:

Sample Question 1
Sequences Medium • Quantitative Aptitude Test
Find the sum of the first 10 terms of the arithmetic sequence: , 7, 12, 17, \dots$
A 240
B 245
C 250
D 260
โœ“ Correct Answer: B - 245
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
The first term is = 2$, common difference = 7 - 2 = 5$, and number of terms = 10$. Using the sum formula for an arithmetic progression: \[S_n = \frac{n}{2}[2a + (n-1)d]\] \[S_{10} = \frac{10}{2}[2(2) + (10-1)5] = 5[4 + 45] = 5 \times 49 = 245\] Thus, the correct option is (B).
Sample Question 2
Sequences Hard • Quantitative Aptitude Test
Find the 100th term of the arithmetic sequence: $15, 20, 25, 30, \dots$
A 500
B 510
C 520
D 530
โœ“ Correct Answer: B - 510
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
First term $a = 15$ and common difference $d = 20 - 15 = 5$. The $n$-th term is $a_n = a + (n-1)d$. For $n = 100$: \[a_{100} = 15 + (100 - 1) \times 5 = 15 + 99 \times 5 = 15 + 495 = 510\] Thus, the correct option is (B).
Sample Question 3
Sequences Medium • Quantitative Aptitude Test
Find the sum of the first $50$ odd positive integers: $1 + 3 + 5 + 7 + \dots$
A 2400
B 2450
C 2500
D 2600
โœ“ Correct Answer: C - 2500
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
The sum of the first $n$ odd positive integers is given by $S_n = n^2$. For $n = 50$: \[S_{50} = 50^2 = 2500\] Or using arithmetic series formula: $S_{50} = \frac{50}{2}[2(1) + (50-1)2] = 25[2 + 98] = 25 \times 100 = 2500$. Thus, the correct option is (C).
Sample Question 4
Sequences Hard • Quantitative Aptitude Test
Find the 8th term in the geometric progression: $1, 3, 9, \dots$
A 2000
B 2187
C 2200
D 2500
โœ“ Correct Answer: B - 2187
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
First term $a = 1$, common ratio $r = 3$. The 8th term is: \[a_8 = a r^{8-1} = 1 \times 3^7 = 2187\] Thus, the correct option is (B).
Sample Question 5
Sequences Hard • Quantitative Aptitude Test
In the geometric sequence $6, 12, 24, \dots$, what is the position (term number) of the value $1536$?
A 7th
B 8th
C 9th
D 10th
โœ“ Correct Answer: C - 9th
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
Here first term $a = 6$ and common ratio $r = \frac{12}{6} = 2$. The $n$-th term is: \[a_n = a r^{n-1} \implies 1536 = 6 \times 2^{n-1} \implies 2^{n-1} = \frac{1536}{6} = 256\] Since $256 = 2^8$, we have $n - 1 = 8 \implies n = 9$. Thus, the correct option is (C).
Sample Question 6
Sequences Hard • Quantitative Aptitude Test
Find the sum of the infinite geometric progression: $\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \dots$
A 1/3
B 1/2
C 2/3
D 1
โœ“ Correct Answer: B - 1/2
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
Here $a = \frac{1}{3}$ and common ratio $r = \frac{1}{3}$. Using $S_\infty = \frac{a}{1 - r}$: \[S_\infty = \frac{1/3}{1 - 1/3} = \frac{1/3}{2/3} = \frac{1}{2}\] Thus, the correct option is (B).
Sample Question 7
Sequences Hard • Quantitative Aptitude Test
In the geometric sequence $1, 3, 9, 27, \dots$, find the common ratio ($r$).
A 2
B 3
C 6
D 9
โœ“ Correct Answer: B - 3
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
The common ratio $r$ is the quotient of any term divided by the preceding term: \[r = \frac{3}{1} = \frac{9}{3} = \frac{27}{9} = 3\] Thus, the correct option is (B).
Sample Question 8
Sequences Hard • Quantitative Aptitude Test
Find the value of the 10th term in the geometric sequence: $1, 3, 9, \dots$
A $3^8$
B $3^9$
C $3^{10}$
D $3^{11}$
โœ“ Correct Answer: B - $3^9$
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
Here the first term is $a_1 = 1$ and common ratio is $r = \frac{3}{1} = 3$. The $n$-th term is $a_n = a_1 r^{n-1}$. For $n = 10$: \[a_{10} = 1 \times 3^{10-1} = 3^9\] Thus, the correct option is (B).
Sample Question 9
Sequences Medium • Quantitative Aptitude Test
If the first term of a geometric sequence is $a_1 = 6$ and the common ratio is $r = 2$, find the 9th term.
A 768
B 1024
C 1536
D 3072
โœ“ Correct Answer: C - 1536
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
The formula for the $n$-th term of a geometric progression is $a_n = a_1 r^{n-1}$. For $n = 9$: \[a_9 = 6 \times 2^{9-1} = 6 \times 2^8 = 6 \times 256 = 1536\] Thus, the correct option is (C).
Sample Question 10
Sequences Hard • Quantitative Aptitude Test
Calculate the sum of the infinite geometric series: $\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \dots$
A 1/3
B 1/2
C 2/3
D 1
โœ“ Correct Answer: B - 1/2
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
The first term is $a = \frac{1}{3}$ and common ratio is $r = \frac{1/9}{1/3} = \frac{1}{3}$. Using the infinite sum formula $S_\infty = \frac{a}{1 - r}$: \[S_\infty = \frac{\frac{1}{3}}{1 - \frac{1}{3}} = \frac{\frac{1}{3}}{\frac{2}{3}} = \frac{1}{2}\] Thus, the correct option is (B).
Practice All 10 Questions Interactively Test your knowledge in real-time with continuous progress saving, instant scoring, and performance analytics.