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

The area of an equilateral triangle with side length 6 cm is:

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What is the probability of drawing a king from a standard deck of 52 playing cards?

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If the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

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

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If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

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What is the sum of the first 10 positive even numbers?

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How many diagonals does a pentagon have?

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

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If x^2 + 4x + 4 = 0, what is the value of x?

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If the average of five consecutive odd numbers is 25, what is the largest number?

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