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 the radius of a circle is 7 cm, what is its circumference?

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If x:y = 4:5 and y:z = 2:3, what is x:z?

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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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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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What is the value of x if log(x) + log(4) = log(32)?

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If the sum of the angles of a polygon is 1080°, how many sides does the polygon have?

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How many diagonals does a pentagon have?

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If a:b = 5:7 and b:c = 6:11, what is a:c?

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

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If a = 2 and b = 3, what is the value of (a^2 + b^2)?

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