Geometric sequence

Question

Maria plans to double the amount of time she spends walking per day each week. She starts to walk 5min. per day on week 1.  After 7 days, she then walks 10 min. per day, etcetera.

a) how many minutes per day will Maria be walking on Week 6?

 

b)  How many minutes per day would Maria be walking on Week 10? 

Why is this not a viable answer?

 

Please show me how to calculate the answers.  Thank you.

Answer 1

The formula for a geometric sequence is:

a_n=a₁*r^n-1

 

a1 is the first term (5)

r is the "common ratio", what you multiply by to get to the next term (2)

n is the term number that you want (6, and then 10).

 

So for week 6:

a₆=5*2^(6-1)=5*32=160 minutes

 

Do the same thing for week 10, and you'll get the other answer, and you'll see why it's unreasonable.

 

Another approach for relatively short sequences is to simply write them out:

5, 10, 20, 40, 80, 160

 

You can see the 6th week has 160 minutes.  

 

This method becomes impractical when determining the 157th term...