$\"\"$

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Consider the choice A:

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The sequence is $\"\"$ .

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Find whether the sequence is arithmetic or geometric sequence.

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Find the common difference of first two terms.

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$\"\"$

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Find the common difference of second and third terms.

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$\"\"$

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Since $\"\"$ , 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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The total amount at the end of $\"\"$ days is $\"\"$ .

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$\"\"$

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Consider the choice B:

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The sequence is $\"\"$ .

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Find whether the sequence is arithmetic or geometric sequence.

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Find the common difference of first two terms.

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$\"\"$

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Find the common difference of second and third terms.

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$\"\"$

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Since $\"\"$ , the sequence is a not arithmetic sequence.

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Find the common ratio of first two terms.

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$\"\"$

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$\"\"$ .

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Find the common difference of second and third terms.

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$\"\"$

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$\"\"$ .

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Since $\"\"$ , the sequence is a geometric sequence.

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

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

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

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$\"\"$

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The total amount at the end of $\"\"$ days is $\"\"$ .

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As $\"\"$ , the choice B receives more money.

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$\"\"$

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Choice A: The total amount at the end of $\"\"$ days is $\"\"$ .

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Choice B: The total amount at the end of $\"\"$ days is $\"\"$ .

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The choice B receives more money.