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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A rectangle has a length of 10 cm and a width of 5 cm. What is the diagonal of the rectangle?

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If sin(A) = 1/2 and A is acute, what is the value of A?

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If 2a + b = 10 and a - b = 4, what is the value of a?

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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 = 2 and b = 3, what is the value of (a^2 + b^2)?

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What is the area of a circle with a diameter of 14 cm?

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If the perimeter of a square is 36 cm, what is the length of its diagonal?

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What is the sum of the interior angles of a hexagon?

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What is the cube of 4?

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