Write the First Five Terms of the Sequence $a _ { n } = \frac { ( - 1 ) ^ { n + 4 } } { n ^ { 2 } + 1 }$

question 63

Multiple Choice

Write the first five terms of the sequence $a _ { n } = \frac { ( - 1 ) ^ { n + 4 } } { n ^ { 2 } + 1 }$ . Assume that n begins with 1.

• A) \(a _ { 1 } = - \frac { 1 } { 2 } , a _ { 2 } = \frac { 1 } { 5 } , a _ { 3 } = - \frac { 1 } { 10 } , a _ { 4 } = \frac { 1 } { 17 } , a _ { 5 } = - \frac { 1 } { 26 }\)
• B) \(a _ { 1 } = \frac { 1 } { 2 } , a _ { 2 } = \frac { 1 } { 5 } , a _ { 3 } = \frac { 1 } { 10 } , a _ { 4 } = \frac { 1 } { 17 } , a _ { 5 } = \frac { 1 } { 26 }\)
• C) \(a _ { 1 } = - 1 , a _ { 2 } = \frac { 1 } { 4 } , a _ { 3 } = - \frac { 1 } { 9 } , a _ { 4 } = \frac { 1 } { 16 } , a _ { 5 } = - \frac { 1 } { 25 }\)
• D) \(a _ { 1 } = \frac { 1 } { 2 } , a _ { 2 } = - \frac { 1 } { 5 } , a _ { 3 } = \frac { 1 } { 10 } , a _ { 4 } = - \frac { 1 } { 17 } , a _ { 5 } = \frac { 1 } { 26 }\)
• E) \(a _ { 1 } = 1 , a _ { 2 } = - \frac { 1 } { 4 } , a _ { 3 } = \frac { 1 } { 9 } , a _ { 4 } = - \frac { 1 } { 16 } , a _ { 5 } = \frac { 1 } { 25 }\)

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Definitions:

Equilibrium Quantity

The supply and demand of goods or services at the price where they are balanced.

Marginal Productivity

The additional output derived from the use of one more unit of a variable input while other inputs remain constant.

Equilibrium Wage Rate

The equilibrium wage rate is the wage level at which the quantity of labor supplied by workers equals the quantity of labor demanded by employers in the market.

Marginal Productivity

The change in output resulting from employing one more unit of a particular input, keeping all other inputs constant.