Write a recursive rule and an explicit rule for an arithmetic sequence that models a situation. Then use the rule to answer the question. Jack begins

Lewis Harvey 2021-02-19 Answered
Write a recursive rule and an explicit rule for an arithmetic sequence that models a situation. Then use the rule to answer the question. Jack begins an exercise routine for 10 minutes each day. Each week he plans to add 10 minutes per day to his exercise routine. For how many minutes will he exercise for each day on the 7th week?
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Expert Answer

Maciej Morrow
Answered 2021-02-20 Author has 98 answers

If Jack exercises for 10 minutes for the first day, then the first term of the sequence is a1=10.
If he adds 10 minutes to his exercise routine each day, then the sequence is arithmetic since it has a common difference of d=10.
The recursive formula for an arithmetic sequence is an=an1+d, n2.

Since d=10, the the recursive formula is then a1=10, an=an1+10,n2
The explicit formula for an arithmetic sequence is an=a1+(n1)d.

Since a1=10 and d=10, then an=10+(n1)(10).
Disturbing the 10 gives an=10+10n10. Combining like terms then gives an=10n.
The 7th week is when n=7. Substituting n=7 into an=10n the gives a7=10×7=70. He will then exercise for 70 min in the 7th week.

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