Question

Which term and geometric sequence are described by the explicit formula aₙ = -6 ⋅ 2ⁿ⁻¹?

A) The nth term and a divergent geometric sequence with a common ratio of 2.
B) The first term and a convergent geometric sequence with a common ratio of -6.
C) The nth term and a convergent geometric sequence with a common ratio of 2.
D) The first term and a divergent geometric sequence with a common ratio of -6.

Answer 1

The expression aₙ = -6 ⋅ 2ⁿ⁻¹ represents the nth term of a geometric sequence. The first term is -6, and the common ratio is 2.

Step-by-step explanation:

The explicit formula, aₙ = -6 ⋅ 2ⁿ⁻¹, represents the nth term of a geometric sequence. In this sequence, each term is found by multiplying the previous term by a constant ratio. To determine the term and the common ratio, we can rewrite the formula as aₙ = -6 ⋅ (2)ⁿ ⋅ (2)⁻¹. This shows that the first term is -6, and the common ratio is 2. Therefore, the correct answer is D) The first term and a divergent geometric sequence with a common ratio of -6.