Topic Details (Notes format)

How to Identify Arithmetic vs. Geometric Sequences

Subject: Mathematics

Book: Maths Mastery

Arithmetic sequences have a constant difference (d) between terms (e.g., 3, 7, 11, ...), while geometric sequences have a constant ratio (r) between terms (e.g., 3, 6, 12, 24, ...). You can test by subtracting consecutive terms for arithmetic or dividing consecutive terms for geometric. Recognizing the sequence type helps select the correct sum formula: Sₙ(arithmetic) = (n/2)(2a₁ + (n–1)d), Sₙ(geometric) = a₁(1–rⁿ)/(1–r). These sequences model linear and exponential growth, vital in finance (loan payments vs. compound interest) and advanced math topics (series expansions, signals).

Practice Questions

What is the HCF of 72 and 120?

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The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

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If the sum of three consecutive integers is 72, what are the integers?

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A car travels 240 km in 4 hours. What is its average speed?

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If a square has a perimeter of 64 cm, what is its area?

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What is the LCM of 15 and 20?

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If sin(θ) = 0.6 and θ is acute, what is cos(θ)?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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If x - y = 5 and x + y = 15, what is the value of x?

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

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