Find the Fourth Term of the Recursively Defined Infinite Sequence $$a _ { 1 } = 110 , a _ { k + 1 } = \frac { 1 } { 2 } a _ { k }$$

question 19

Multiple Choice

Find the fourth term of the recursively defined infinite sequence. $$a _ { 1 } = 110 , a _ { k + 1 } = \frac { 1 } { 2 } a _ { k }$$

• A) \(a _ { 4 } = 17 \frac { 3 } { 4 }\)
• B) \(a _ { 4 } = 18 \frac { 3 } { 16 }\)
• C) \(a _ { 4 } = 13 \frac { 3 } { 4 }\)
• D) \(a _ { 4 } = \frac { 3 } { 4 }\)
• E) \(a _ { 4 } = 18 \frac { 3 } { 4 }\)

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Definitions:

Higher Price

A situation where the cost of a good or service is increased beyond its standard or previous rate.

Economic Profit

The difference between total revenue and total costs, including both explicit and implicit costs, indicating the financial gain exceeding opportunity costs.

Marginal Revenue

The extra revenue received from the sale of an additional unit of a product or service.

Competitive Price-searcher

A market participant who actively seeks out the best price for goods or services among various competitors.