The Sequence Is Defined Recursively $a _ { 1 } = - 2 ; a _ { n } = \sqrt { a _ { 2 } ^ { n - 1 } + 1 } , n \geq 2$

question 25

Multiple Choice

The sequence is defined recursively. Compute the first five terms of the sequence. $a _ { 1 } = - 2 ; a _ { n } = \sqrt { a _ { 2 } ^ { n - 1 } + 1 } , n \geq 2$

• A) \(- 2 , \sqrt { 5 } , \sqrt { 6 } , \sqrt { 5 } , \sqrt { 2 }\)
• B) \(- 2 , \sqrt { 10 } , \sqrt { 6 } , \sqrt { 7 } , 4 \sqrt { 2 }\)
• C) \(- 2 , \sqrt { 5 } , \sqrt { 6 } , \sqrt { 7 } , 2 \sqrt { 2 }\)
• D) \(- 2 , \sqrt { 5 } , \sqrt { 3 } , \sqrt { 7 } , 2 \sqrt { 8 }\)
• E) \(- 2 , \sqrt { 5 } , \sqrt { 3 } , \sqrt { 7 } , \sqrt { 2 }\)

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Definitions:

Base Year

A specific year against which economic growth is measured, serving as a standard comparison for other years in index calculations and real values.

Real GDP

Gross Domestic Product adjusted for inflation, reflecting the value of all goods and services produced by an economy in a given year.

Inflation

A measure of the rate at which the general level of prices for goods and services is rising, leading to a decrease in purchasing power.

National Income

The total value of all goods and services produced by a country's residents and businesses, including income from abroad, over a specified period.