Progressions — Syllabus
Telangana Board · Class 10 · Mathematics
What Progressions covers in Telangana Board Class 10 Mathematics: 4 topics, for the 2026-27 session. Topics include Arithmetic Progression: Core Idea, Nth.
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Topics in Progressions
Arithmetic Progression: Core Idea
- An Arithmetic Progression is a list of numbers in which each term after the first is obtained by adding a fixed number to the preceding term.
- The fixed number is called the common difference.
- An AP can be finite or infinite.
Nth Term of an Arithmetic Progression
- The nth term of an AP gives any term directly without writing all earlier terms.
- If there are n terms in the AP, then the nth term is also the last term, sometimes denoted by l.
- The formula is used in salary growth, distances, savings, and counting terms in a sequence.
Sum of First n Terms of an Arithmetic Progression
- The sum of terms in an AP can be found quickly without adding each term one by one.
- The Gauss pairing idea shows how sums can be simplified by pairing first and last terms.
- There are two useful sum formulas: one using a and d, and one using a and l.
Geometric Progression: Core Idea and nth Term
- A Geometric Progression is a list in which each term after the first is obtained by multiplying the preceding term by a fixed non-zero number.
- The fixed number is called the common ratio.
- A GP requires a not equal to 0, r not equal to 0, and r not equal to 1.
Key Concepts
Central concept: Progressions
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