$\"\"$

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Meg plans to run $\"\"$ the first day, $\"\"$ the second day, $\"\"$ the third day and so on.

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Therefore, $\"\"$ and $\"\"$ .

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Find the common difference $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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The series is arithmetic series.

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(a) Find the number of miles meg will run on $\"\"$ day.

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Formula for $\"\"$ term of the arithmetic series is $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The number of miles meg will run on $\"\"$ day is $\"\"$ .

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$\"\"$

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(b) Find how many days will take to meg will reach $\"\"$ .

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Find the term that corresponds to $\"\"$ .

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formula for sum of arithmetic series is $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ and $\"\"$

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$\"\"$ and $\"\"$ .

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Since the number of days should not be negative.

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Therefore, $\"\"$ .

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Meg will reach her goal of $\"\"$ total miles on $\"\"$ .

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$\"\"$

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(a) The number of miles meg will run on $\"\"$ day is $\"\"$ .

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(b) Meg will reach her goal of $\"\"$ total miles on $\"\"$ .