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

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

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What is the remainder when 5^100 is divided by 3?

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If the average of five consecutive odd numbers is 25, what is the largest number?

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

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If the cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

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If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

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

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If the sum of the squares of two consecutive positive integers is 365, what are the integers?

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What is the sum of all angles in a hexagon?

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If two complementary angles differ by 30°, what are the angles?

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