# 11.5.4. Arithmetic Series

A runner is practicing for a long distance race, where the plan is to run km on the first day and to do 0.7 kilometers more every day. In how many days will the runner cover the distance of km provided that the plan is followed properly?

• A8 days
• B24.1 days
• C4 days
• D13 days

### Example

A runner is practicing for a long distance race, where the plan is to run km on the first day and to do 0.7 kilometers more every day. In how many days will the runner cover the distance of km provided that the plan is followed properly?

### Solution

Remember the sum of an arithmetic series is given by where is the first term, and is the common difference. For the series we have been given, and . Hence,

To find how many days it will take for the runner to cover km, we solve the following equation for :

We can solve this equation using the quadratic formula:

Since must be a positive number, then . Hence, the runner needs 8 days to cover km.

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