Find a Formula for the Nth Term of the Sequence $a _ { n } = 1 + ( - 1 ) ^ { n ( n + 1 ) / 2 }$

question 468

Multiple Choice

Find a formula for the nth term of the sequence.
-0, 2, 2, 2, 0, 2, 2, 2 (0, 2, 2, 2 repeated)

• A) \(a _ { n } = 1 + ( - 1 ) ^ { n ( n + 1 ) / 2 }\)
• B) \(a _ { n } = 1 + ( - 1 ) ^ {{ n } ( n - 1 ) / 2}\)
• C) \(a _ { n } = 1 + ( - 1 ) ^ {{ n } ( n + 1 ) ( n + 2 ) / 6}\)
• D) \(a _ { n } = 1 + ( - 1 ) ^ { ( n + 1 ) ( n + 2 ) / 2 }\)

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Definitions:

Marginal Cost

The rise in overall expenses associated with the production of an extra unit of a product or service.

Average Total Cost

The total cost of production divided by the number of units produced, giving a per unit cost of production.

Marginal Cost

The expense associated with creating an extra unit of a product or service.

Marginal Cost

The cost of producing one additional unit of a good or service, often varying with the level of production.