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

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

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What is the HCF of 48 and 180?

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

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

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If the length of a rectangle is doubled and the width is halved, what is the change in area?

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If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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The base of a triangle is 10 cm and its height is 6 cm. What is its area?

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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 the probability of an event is 1/4, what is the probability of its complement?

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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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