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After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests you start by jogging for 14 minutes each day. Each week after, he suggests that you increase your daily jogging time by 7 minutes. How many weeks before you are up to jogging 70 minutes?

Answer :

Given that initial time for jogging is,

[tex]a_{_1}=14[/tex]

After each week the time is increased by

[tex]d=7[/tex]

This gives an arithmetic sequence.

To find n such that,

[tex]a_n=70[/tex]

Therefore,

[tex]\begin{gathered} a_n=a_1+(n-1)d \\ n=\frac{a_n-a_1}{d}+1 \end{gathered}[/tex]

So,

[tex]\begin{gathered} n=\frac{70-14}{7}+1 \\ =\frac{56}{7}+1 \\ =8+1 \\ =9 \end{gathered}[/tex]

Therefore, 9 weeks before you are up to jogging 70 minutes.

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