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

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 a cylinder has a radius of 7 cm and height of 10 cm, what is its volume?

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If log(100) = 2 and log(10) = 1, what is log(1000)?

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

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What is the square root of 144?

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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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If a = 4 and b = 5, what is the value of (a+b)^2?

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If x:y = 2:3 and z:y = 4:3, what is x:z?

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If x^2 - 5x + 6 = 0, what are the roots?

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A triangle has angles 60°, 60°, and 60°. What type of triangle is it?

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