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

The perimeter of a rectangle is 40 cm, and its length is 12 cm. What is its width?

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A sphere has a radius of 7 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 7th term of the arithmetic progression 3, 6, 9, 12,...?

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A sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?

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What is the area of an equilateral triangle with side length 10 cm?

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If sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?

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The probability of rolling a sum of 7 with two dice is:

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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 x + 1/x = 5, what is the value of x^2 + 1/x^2?

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