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Predicting What Comes Next: Exploring Sequences and Progressions
Sequences help us study numbers or quantities arranged in a particular order. In exams, students are usually asked to identify the pattern, find a missing term, write a rule, or decide whether the situation follows addition or multiplication. Progressions are special sequences with a regular pattern. Arithmetic progressions use a constant difference, while geometric progressions use a constant ratio. This chapter builds careful thinking for formula use, word problems, and pattern-based reasoning.
Difficulty
Medium
Study time
60-80 min
Plan by time
Pick the window that matches what you have right now.
If you have 15 min
Last-pass revision
Skim the Quick Revision table — definitions, formulas, and the traps board examiners reuse.
Open Quick RevisionIf you have 45 min
Targeted practice
Read the high-priority concepts, then take the chapter MCQ quiz to find weak spots.
Start MCQ QuizIf you have 60 min
First full pass
Walk every concept in chapter order, then revise and quiz. Best for the first time you study this chapter.
Open Key ConceptsChapter Learning Map
Start with one of the buckets below, then open the full map when you want the complete concept roadmap.
Key Concepts
Concepts grouped the way the chapter is taught — open the bucket that matches what you want to revise.
Core Concepts
high priorityOpen the chapter concepts in a clean revision order.
What is a Sequence?
A sequence is an ordered list of numbers, objects, or quantities written according to a rule or pattern.
Explicit (Direct) Rule for a Sequence
An explicit rule gives the value of any term directly using its position number n.
Recursive Rule
A recursive rule defines each term of a sequence using one or more previous terms, along with a starting term.
Arithmetic Progression — Definition
An arithmetic progression is a sequence in which the difference between every two consecutive terms is constant.
Sum of First n Terms of an AP
The sum of the first n terms of an arithmetic progression is the total obtained by adding its first n terms.
Geometric Progression — Definition
A geometric progression is a sequence in which each term is obtained by multiplying the previous term by the same non-zero constant ratio.
Real-World Applications of Sequences
Real-world applications of sequences use ordered patterns to model repeated changes in money, distance, growth, decay, arrangements, or daily-life quantities.
Exam Intelligence
Use this section to decide what deserves the most revision time.
High Probability Topics
- What is a Sequence?
- Explicit (Direct) Rule for a Sequence
- Recursive Rule
- Arithmetic Progression — Definition
- Sum of First n Terms of an AP
- Geometric Progression — Definition
- Real-World Applications of Sequences
Common Traps
- Treating an ordered sequence like an unordered set.
- Substituting term value instead of position number n.
- Forgetting the starting term in recursive rules.
- Ignoring the negative sign in a decreasing AP.
- Using n instead of n - 1 in nth-term formulas.
- Using the last visible term as l without checking whether it is the required last term.
- Confusing constant difference with constant ratio.
- Choosing AP or GP in word problems without reading the change phrase.
Likely Question Types
- MCQ: concept checks, applications, and common mistakes
- Very short answer: definitions, formulas, or conditions
- Short answer: worked method, example, or reason-based explanation
- Case-based: chapter scenario with concept-linked subparts
Quick Revision
Concept, formula or equation to remember, and the trap that loses marks — in one scannable view.
- A sequence is an ordered list, so term position is important.
- An explicit rule gives a term directly from n.
- A recursive rule needs a starting term and a rule from the previous term.
- An AP has a constant common difference and uses an = a + (n - 1)d.
- The sum of first n AP terms can be found without adding every term.
- A GP has a constant common ratio and uses an = a · r^(n - 1).
- Real-life sequence questions become easier after deciding AP or GP first.
- What is a Sequence?: A sequence is an ordered list of numbers, objects, or quantities written according to a rule or pattern.
Practice
Use short concept checks first, then move into the full chapter test.
Free Chapter MCQ Quiz
Try a 15-question quiz from this chapter. Get instant score and unlock concept-wise analytics.
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