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

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If the perimeter of a square is 40 cm, what is the area of the square?

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If the product of two numbers is 120 and their sum is 26, what are the numbers?

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What is the HCF of 72 and 120?

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If the sum of three consecutive integers is 96, what are the integers?

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A man rows downstream at 6 km/h and upstream at 4 km/h. What is the speed of the stream?

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A sum triples in 20 years at simple interest. What is the rate of interest per annum?

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The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

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

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If a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?

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