Prove the Following Statement by Mathematical Induction $1+7+13+\ldots+(6 n-5)=n(3 n-2)$

question 46

Essay

Prove the following statement by mathematical induction. $1+7+13+\ldots+(6 n-5)=n(3 n-2)$

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Definitions:

Dimethylbutane

An organic compound with the formula C6H14, a type of alkane that is used as a fuel.

Dimethylpentane

An isomer of hexane, used as a reference fuel in octane rating and found in various petroleum distillates.

Ethylbutane

A chemical compound that is a structural isomer of octane, with the formula C6H14.

Tetramethylbutane

An organic compound with a formula of C8H18, known as a highly branched alkane used in chemical research and applications.