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Which formula can be used to sum the first n terms of a geometric sequence?

a. Sₙ = a(1 - rⁿ)/(1 - r)
b. Sₙ = a + ar + ar² + ... + arⁿ
c. Sₙ = a.rⁿ
d. Sₙ = a(1 - r)/(1 - rⁿ)

1 Answer

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Final answer:

The correct formula to sum the first n terms of a geometric sequence is S₍ = a(1 - rⁿ)/(1 - r), which is represented by option a in the student's question.

Step-by-step explanation:

The formula to sum the first n terms of a geometric sequence is S₍ = a(1 - rⁿ)/(1 - r), where a is the first term of the sequence, r is the common ratio, and n is the number of terms. This formula assumes that the common ratio r is not equal to 1, since that would result in a division by zero error. If the common ratio r is equal to 1, then all terms of the sequence are equal and the sum of the first n terms is simply n times the common term.If we apply option a. S₍ = a(1 - rⁿ)/(1 - r), we find that this is indeed the correct formula for the sum of the first n terms of a geometric sequence.

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