Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What formula defines a geometric sequence?

sⁿ = a₁(1 + rⁿ)/(1 + r)
sⁿ = a₁(1 - rⁿ)/(1 - r)
sⁿ = a₁(1 + r)/(1 - r)
sⁿ = a₁(1 - r)/(1 + r)

The correct answer is: sⁿ = a₁(1 - rⁿ)/(1 - r)

The correct answer is based on the formula that defines the sum of a geometric series. A geometric sequence is formed by multiplying each term by a constant ratio. The sum of the first n terms of a geometric sequence can be represented using the formula: sⁿ = a₁(1 - rⁿ) / (1 - r) where: - sⁿ is the sum of the first n terms - a₁ is the first term of the sequence - r is the common ratio between consecutive terms - n is the number of terms This formula is applicable when the common ratio (r) is not equal to 1. It effectively captures how the terms in a geometric sequence accumulate when added together. If r were equal to 1, each term would simply be equal to a₁, resulting in a linear sequence rather than a geometric one. Other options proposed different formulas that do not align with the definition and properties of a geometric series. The correct answer provides a clear representation of the sum of the geometric sequence, thus helping to identify the finite series and understand how the sequence behaves mathematically.