Sequences and Series | AP, GP, nth term, sum formulae

A sequence is an ordered list of numbers following a specific rule, while a series is the sum of those terms. This lesson covers the definitions, formulas, and solving techniques for the two most common types of progressions encountered in algebra: Arithmetic Progressions (AP) and Geometric Progressions (GP). Here is the specific content covered in this lesson: • Arithmetic Progressions (AP): * Understanding sequences where each term is found by adding a constant value, called the common difference (d), to the preceding term. • The formula for finding the n-th term of an AP: Tn = a + (n - 1)d, where 'a' is the first term. • The formulas for calculating the sum of the first n terms (Sn). • Geometric Progressions (GP): * Understanding sequences where each term is found by multiplying the preceding term by a constant value, called the common ratio (r). • The formula for finding the n-th term of a GP: Tn = a * r^(n-1). • The formulas for calculating the sum of the first n terms (Sn), depending on whether the common ratio 'r' is greater than or less than 1. • Sum to Infinity (S_infinity): * Explaining the condition required for a geometric series to converge (where 'r' is between -1 and 1) and how to calculate the sum of an infinite number of terms using the formula: S_infinity = a / (1 - r). #Mathematics #SequencesAndSeries #ArithmeticProgression #GeometricProgression #Algebra #HighSchoolMath #STEM