Chapter Hub
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.
Sequence Foundations
Covers What is a Sequence?, Explicit (Direct) Rule for a Sequence and Recursive Rule.
Open mapArithmetic Progression
Covers Arithmetic Progression — Definition and Sum of First n Terms of an AP.
Open mapGeometric and Applied Patterns
Covers Geometric Progression — Definition and Real-World Applications of Sequences.
Open mapKey Concepts
Concepts grouped the way the chapter is taught — open the group that matches what you want to revise.
Sequence Foundations
Covers What is a Sequence?, Explicit (Direct) Rule for a Sequence and Recursive Rule.
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
Covers Arithmetic Progression — Definition and Sum of First n Terms of an AP.
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 and Applied Patterns
Covers Geometric Progression — Definition and Real-World Applications of Sequences.
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
The traps that cost marks in this chapter, and how its main concepts turn up in the paper.
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.
How CBSE Asks This Chapter
- What is a Sequence?
Students may be given a list such as 6, 11, 16, 21 and asked to find the next term, identify a particular term, or describe the pattern.
- Explicit (Direct) Rule for a Sequence
Questions may ask students to find a specific term, complete a table of n and an, or check whether a given number can be a term.
- Recursive Rule
Students may be asked to generate the first few terms from a recursive rule or write a recursive rule from a given pattern.
- Arithmetic Progression — Definition
Students may be asked to verify whether a list is an AP, find d, find the nth term, or find a missing term.
Quick Revision
Concept, formula or equation to remember, and the trap that loses marks — in one scannable view.
Remember
A sequence is commonly written as a1, a2, a3, ..., an, where an means the term in the nth position.Trap to avoid
Students often look only at the numbers and ignore their positions, so they may reverse the sequence or choose a term without checking its place.
Explicit (Direct) Rule for a Sequence
Remember
Explicit form: an = expression in n.Trap to avoid
Students sometimes substitute the term value in place of n, but n represents the position, not the term itself.
Remember
Typical recursive form: a1 = starting value, an = an-1 + d for n greater than 1.Trap to avoid
Students write only the changing rule but forget the starting term, so the sequence cannot be fixed uniquely.
Arithmetic Progression — Definition
Remember
For an AP, d = next term - previous term and an = a + (n - 1)d.Trap to avoid
Students sometimes compare non-consecutive terms or use only one pair of terms and conclude too quickly.
Remember
Sn = n/2 × (2a + (n - 1)d) and Sn = n/2 × (a + l), where l is the nth or last required term.Trap to avoid
Students sometimes use the last visible term as l even when the question asks for more terms than shown.
Geometric Progression — Definition
Remember
For a GP, r = next term ÷ previous term and an = a · r^(n - 1).Trap to avoid
Students sometimes subtract consecutive terms and call it GP, but GP depends on ratio, not difference.
Real-World Applications of Sequences
Remember
AP model: an = a + (n - 1)d.Trap to avoid
Students often start calculating without deciding whether the situation uses a constant difference or a constant ratio.
| Concept | Remember | Trap to avoid |
|---|---|---|
| What is a Sequence? | A sequence is commonly written as a1, a2, a3, ..., an, where an means the term in the nth position. | Students often look only at the numbers and ignore their positions, so they may reverse the sequence or choose a term without checking its place. |
| Explicit (Direct) Rule for a Sequence | Explicit form: an = expression in n. | Students sometimes substitute the term value in place of n, but n represents the position, not the term itself. |
| Recursive Rule | Typical recursive form: a1 = starting value, an = an-1 + d for n greater than 1. | Students write only the changing rule but forget the starting term, so the sequence cannot be fixed uniquely. |
| Arithmetic Progression — Definition | For an AP, d = next term - previous term and an = a + (n - 1)d. | Students sometimes compare non-consecutive terms or use only one pair of terms and conclude too quickly. |
| Sum of First n Terms of an AP | Sn = n/2 × (2a + (n - 1)d) and Sn = n/2 × (a + l), where l is the nth or last required term. | Students sometimes use the last visible term as l even when the question asks for more terms than shown. |
| Geometric Progression — Definition | For a GP, r = next term ÷ previous term and an = a · r^(n - 1). | Students sometimes subtract consecutive terms and call it GP, but GP depends on ratio, not difference. |
| Real-World Applications of Sequences | AP model: an = a + (n - 1)d. | Students often start calculating without deciding whether the situation uses a constant difference or a constant ratio. |
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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