This section provides step-by-step examples on how to analyze ordered lists of numbers. You will learn to find specific terms and sums of arithmetic and geometric sequences, evaluate infinite series, and expand binomials using the Binomial Theorem.

Arithmetic Progression: Finding the n-th Term (Basic)

Problem: Find the 1515th term of the arithmetic sequence: 4,7,10,13,…4, 7, 10, 13, \dots

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Arithmetic Progression: Finding the Number of Terms (Intermediate)

Problem: How many terms are in the arithmetic sequence: 5,9,13,…,815, 9, 13, \dots , 81?

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Arithmetic Series: Sum of an Arithmetic Series (Advanced)

Problem: Find the sum of the first 5050 odd positive integers.

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Geometric Progression: Finding a Specific Term (Intermediate)

Problem: Find the 77th term of the geometric sequence: 3,−6,12,−24,…3, -6, 12, -24, \dots

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Geometric Series: Infinite Geometric Series (Advanced)

Problem: Find the sum of the infinite geometric series: 10+5+2.5+1.25+…10 + 5 + 2.5 + 1.25 + \dots

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Harmonic Progression: Finding the n-th Term (Intermediate)

Problem: Find the 6th term of the harmonic progression 1/3,1/7,1/11,…1/3, 1/7, 1/11, \dots.

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Binomial Theorem: Expanding a Binomial (Advanced)

Problem: Expand (2x−y)4(2x - y)^4 using the Binomial Theorem.

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