Find an Explicit Rule for the Nth Term of the Sequence

question 69

Multiple Choice

Find an explicit rule for the nth term of the sequence.
-The second and fifth terms of a geometric sequence are 9 and 243 , respectively.

• A) \(a _ { n } = 3 \cdot 3 ^ { n + 3 }\)
• B) \(a _ { n } = 3 \cdot 3 ^ { n - 2 }\)
• C) \(a _ { n } = 3 \cdot 3 ^ { n - 1 }\)
• D) \(a _ { n } = 3 \cdot 3 ^ { n + 1 }\)

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Definitions:

Marginal Cost

The increase in total cost that arises from producing an extra unit of output.

Fixed Cost

Costs that do not vary with the level of production or sales, such as rent, salaries, and insurance.

Cartel

An agreement among competing firms to control prices or exclude entry of a new competitor in a market, often to maximize their profits illegally or unethically.

Collusive Agreements

Arrangements or agreements, often illegal, between competing firms to limit competition, control prices, or divide markets among themselves.