Topic Details (Notes format)

How to Use Summation Formulas for Arithmetic and Geometric Series

Subject: Mathematics

Book: Maths Mastery

Arithmetic series Sₙ= (n/2)(a₁+aₙ) or (n/2)[2a₁+(n–1)d] sums n terms. Geometric series Sₙ= a₁(1–rⁿ)/(1–r) for r≠1. These standard results handle repeated adding or multiplying patterns. For example, if an arithmetic sequence is 5, 8, 11,... with n=6 terms, sum is (6/2)[2×5+(6–1)×3]=3[10+15]=75. Mastery helps with finances (loan amortization), repeated additions in budgeting, or analyzing growth in discrete steps. Summation formulas are cornerstones of advanced math, bridging simple patterns to deep combinatorial or calculus expansions.

Practice Questions

A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

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What is the value of log₃(27)?

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The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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If a:b = 5:7 and b:c = 6:11, what is a:c?

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A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

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What is the HCF of 48 and 180?

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What is the cube of 4?

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A sphere has a radius of 7 cm. What is its volume?

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What is the 7th term of the arithmetic progression 3, 6, 9, 12,...?

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If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

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