05. Arithmetic Progression


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Description:

Arithmetic Progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant. This concept forms the basis for many mathematical problems involving patterns, sums, and sequences. This chapter explains how to identify, analyze, and work with APs using formulas and practical examples.

Why Choose This Topic?

✅ Simple explanation of arithmetic sequences
 ✅ Learn to find the common difference and nth term
 ✅ Understand the formula for the sum of n terms
 ✅ Real-life examples like salary increments and pattern problems
 ✅ Practice problems to build confidence

What’s Inside?

✅ Definition and examples of Arithmetic Progression
 ✅ Formula for the nth term of an AP: an=a+(n−1)da_n = a + (n-1)dan=a+(n−1)d
 ✅ Sum of first n terms: Sn=n2[2a+(n−1)d]S_n = \frac{n}{2}[2a + (n-1)d]Sn=2n[2a+(n−1)d]
 ✅ Word problems and application-based exercises
 ✅ Step-by-step solved examples

Frequently Asked Questions (FAQs)

A sequence where each term differs from the previous one by a constant difference.

Use the formula an = a + (n - 1)d.

Use the formula Sn = (n / 2) [2a + (n - 1)d].

The fixed amount added to get from one term to the next.

Yes, it can be negative, indicating a decreasing sequence.



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