Arithmetic Progression (AP)

Arithmetic Progression (AP)

This lesson covers the following key concepts:

• Definition and general term of AP
• Common difference and its properties
• nth term formula: aₙ = a + (n-1)d
• Sum of n terms of AP
• Sum of first n natural numbers
• Properties of AP (three terms in AP, arithmetic mean)
• Insertion of arithmetic means between two numbers

Important Formulas

• $$a_n = a + (n-1)d$$
• $$S_n = \frac{n}{2}[2a + (n-1)d] = \frac{n}{2}(a + l)$$
• $$\text{AM between } a, b: \frac{a+b}{2}$$
• $$\text{If } a, b, c \text{ in AP: } 2b = a + c$$
• $$\sum_{k=1}^{n} k = \frac{n(n+1)}{2}$$
• $$\text{Insert m AMs: } d = \frac{b-a}{m+1}$$