A Statement $$\mathrm { S } _ { \mathrm { n } }$$

question 26

Essay

A statement
$$\mathrm { S } _ { \mathrm { n } }$$ about the positive integers is given. Write statements
$\mathrm { S } _ { 1 } , \mathrm {~S} _ { 2 }$ and S
$\mathrm { S } _ { 3 }$ , and show that each of these
statements is true.
- $$S _ { n } : 1 ^ { 2 } + 4 ^ { 2 } + 7 ^ { 2 } + \ldots + ( 3 n - 2 ) ^ { 2 } = \frac { n \left( 6 n ^ { 2 } - 3 n - 1 \right) } { 2 }$$

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Definitions:

Return On Sales

A financial ratio that calculates the percentage of sales revenue that has turned into profits, indicating how efficiently a company is operating.

Sales Revenue

The full income received from goods sales or service delivery before taking out any operational costs or expenditures.

Return On Investment

A financial metric that calculates the profitability of an investment by dividing the profit (or loss) by the cost of the investment.

Imputed Interest Rate

An estimated interest rate used when the actual interest rate is not known or is not applicable, often used in lease agreements or for calculating the present value.