Find a Formula for the General Term $a _ { n }$

question 67

Multiple Choice

Find a formula for the general term $a _ { n }$ of the sequence $\left\{ - \frac { 1 } { 2 } , 0 , \frac { 1 } { 10 } , \frac { 2 } { 17 } , \frac { 3 } { 26 } , \ldots \right\}$ .

• A) \(\frac { ( n - 2 ) } { \left( n ^ { 2 } + 1 \right) }\)
• B) \(\frac { ( n - 2 ) } { \left( n ^ { 2 } - 1 \right) }\)
• C) \(\frac { ( n + 2 ) } { \left( n ^ { 2 } + 1 \right) }\)
• D) \(\frac { ( - 1 ) ^ { n } ( n - 2 ) } { \left( n ^ { 2 } + 1 \right) }\)
• E) \(\frac { ( n - 2 ) } { n ^ { 2 } }\)
• F) \(\frac { n } { \left( n ^ { 2 } + 1 \right) }\)
• G) \(\frac { ( n - 1 ) } { \left( n ^ { 2 } + 1 \right) }\)
• H)None of these

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Definitions:

Real GDP

Real Gross Domestic Product (Real GDP) is a measure of a country's economic output adjusted for price changes (inflation or deflation), reflecting the real value of goods and services produced.

Percentage Change

A mathematical calculation that indicates the degree of change over time, expressed as a percentage, used to measure growth or decline in various contexts such as finance, economics, and statistics.

Nominal GDP

The gross domestic product measured in current prices, without adjusting for inflation, reflecting the value of all goods and services produced over a specific time period.

GDP Deflator

An indicator of the price levels for all fresh, domestically created, final goods and services within an economy, utilized to modify nominal GDP for the determination of real GDP.