You visit the Grand Canyon and drop a penny off the edge of a cliff. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on in an arithmetic sequence. What is the total distance the object will fall in 6 seconds?

*Arithmetic sequence.*

a_{n}=a_{1}+(n-1)d

a_{n}=16+(6-1)32=176

The 6th term is 176. Now we are ready to find the sum:

After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests jogging for 12 minutes each day for the first week. Each week thereafter, he suggests that you increase that time by 6 minutes per day. How many weeks will it before you are up to jogging 60 minutes per day?

Adding 6 minutes to the weekly jogging time for each week creates the sequence: 12, 18, 24,...

This sequence is arithmetic.

a_{n}=a_{1}+(n-1)d

60=12+(n-1)6

60=12+6n-6

60-12+6=6n

54=6n

n=9