Herman wants to build his endurance for running this year. the first week he runs 1.5 miles per day, the second week 2 miles per day. if this pattern continues, how many miles a day will he be running during the 10th week?

6 miles per day during the tenth week.

Step-by-step explanation:

Given:

Miles per day in week 1 is,

Miles per day in week 2 is,

So, there is an increase of 2 - 1.5 = 0.5 miles from week 1 to week 2.

Therefore, the given pattern has a common difference of and thus it follows an arithmetic sequence.

The term of an arithmetic sequence is given as:

Here, 'n' represents the week and represents the miles per day in the week 'n'.

Now, we are asked to find the miles per day in week 10.

So,

Plug in 0.5 for 'd' and . This gives,

Therefore, Herman runs 6 miles per day during the tenth week.

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