Question

Determine whether the sequence below is a geometric sequence and, if so, find a formula that describes the sequence.





2, 4, 8, 16, –32, 64, …







A.

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B.

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C.

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D.

The sequence is not a geometric sequence.

Answer 1

2, 4, 8, 16, –32, 64, …

Common ratio = 4/2 = 2

16/8 = 2

But -32/16 = -2.

The ratio is not constant, hence it is not a geometric.

D. The sequence is not a geometric sequence.

Answer 2

The geometric sequence is given by aₙ = 2(2)ⁿ⁻¹

Geometric sequence

A geometric sequence is in the form:

aₙ = a(r)ⁿ⁻¹

Where a is the first term, r is the common difference.

From the sequence 2, 4, 8, 16, 32, 64, …

r = 4/2 = 8/4 = 2

a = 2, hence:

aₙ = 2(2)ⁿ⁻¹

The geometric sequence is given by aₙ = 2(2)ⁿ⁻¹

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