$\"\"$

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The $\"\"$ -years professional football league contract begins with a salary of $\"\"$ per year.

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The contract is over a period of $\"\"$ years.

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Consider the choice 1:

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A bonus of $\"\"$ each year.

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Total salary of the professional football league is $\"\"$ .

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For over $\"\"$ years, the total salary is $\"\"$ .

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$\"\"$

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Consider the choice 2:

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An annual increase of $\"\"$ per year beginning after $\"\"$ year.

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The sequence is a geometric sequence.

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The first term of the sequence is $\"\"$ .

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Therefore, common ratio is $\"\"$

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Find the sum of increments over a period of $\"\"$ -year.

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Formula for sum of $\"\"$ terms in the geometric sequence is $\"\"$ .

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$\"\"$

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Increment in $\"\"$ years in $\"\"$ .

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Total income: $\"\"$ .

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For over $\"\"$ years, the total salary is $\"\"$ .

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$\"\"$

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Consider the choice 3:

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An annual increase of $\"\"$ per year beginning after $\"\"$ year.

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The sequence is a arithmetic sequence.

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Find the sum of $\"\"$ terms in the sequence.

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Formula for sum of $\"\"$ terms in the arithmetic sequence is $\"\"$ where $\"\"$ .

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$\"\"$

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Substitute $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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For over $\"\"$ years, the total salary is $\"\"$ .

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Observe the salaries of the three choices.

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Choice 2 provides more money when compared to others.

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Choice 1 provides least when compared to others.

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Hence, choice 2 is the best method.

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$\"\"$

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Choice 1:

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For over $\"\"$ years, the total salary is $\"\"$ .

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Choice 2:

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For over $\"\"$ years, the total salary is $\"\"$ .

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Choice 3:

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For over $\"\"$ years, the total salary is $\"\"$ .

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Choice 2 provides more money when compared to others.

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Choice 1 provides least when compared to others.

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Choice 2 is the best method.