Write the Word or Phrase That Best Completes Each Statement $$1 ^ { 2 } + 4 ^ { 2 } + 7 ^ { 2 } + \ldots + ( 3 n - 2 ) ^ { 2 } = \frac { n \left( 6 n ^ { 2 } - 3 n - 1 \right) } { 2 }$$

question 139

Essay

Write the word or phrase that best completes each statement or answers the question.
Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers 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:

Accounts Payable

The amounts owed by a business to its suppliers or creditors for goods and services received, representing short-term liabilities.

Accounts Receivable

Funds that are due to a company from its clients for the delivery of goods and services which payment is pending.

Net Assets

The total assets of a company minus its total liabilities; a measure of its financial health and value.

Equity

The value of an owner's interest in a property or business, calculated as the difference between the total assets and total liabilities.