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Arithmetic and geometric progressions

This test develops recognition of arithmetic and geometric progressions and use of general-term formulas. Tasks include finding the common difference or ratio, determining missing terms and calculating sums of initial terms.

Questions: 10Estimated time: 15 minutes

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Sample questions

For an arithmetic progression a1 = ___, d = ___. Find a___.

For an arithmetic progression a₁ = ___, d = ___. Find the sum of the first ___ terms.

The first two arithmetic-progression terms are ___ and ___. Find d.

For a geometric progression b1 = ___, q = ___. Find b___.

For a geometric progression b₁ = ___, q = ___. Find the sum of the first ___ terms.

Arithmetic and geometric progressions

An arithmetic progression has constant difference d: aₙ = a₁ + (n − 1)d, and Sₙ = n(a₁ + aₙ)/2. A geometric progression has constant ratio q: bₙ = b₁qⁿ⁻¹.

Sums and models

For q ≠ 1, its finite sum is Sₙ = b₁(qⁿ − 1)/(q − 1). An infinite sum exists only when |q| < 1 and equals b₁/(1 − q). Distinguish a constant additive change from a constant multiplier before choosing the model.

Arithmetic and geometric progressions

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Sample questions