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 cube has a side length of 4 cm. What is its volume?

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A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

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If a right triangle has legs of 9 cm and 12 cm, what is the length of the hypotenuse?

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What is the cube of 4?

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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If sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?

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What is the sum of the first 20 odd numbers?

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What is the HCF of 48 and 180?

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If x^2 - 5x + 6 = 0, what are the roots?

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

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