The total number of people who have seen a band play as of the 1st of each month follows a geometric sequence.

Question

In March, a total of 2100 people have seen the band perform. In June of that same year, a total of 3150 people have seen the band perform. Assuming this pattern continues, how many people will have seen the band perform as of January 1 of the next year? Round your answer to the nearest person.

Answer 1

 

Let r = common ratio

 

     a₁ = 2100      (March)

     a₂ = 2100r     (April)

     a₃ = 2100r²    (May)

 

     a₄ = 2100•r³   (June)

  3150 = 2100 r³

  3150/2100 = r³

  1.5 = r³

 

  r = (12^1/3)/2

 

Now that we have r, we can determine the formula for the nth term of the sequence

 

     a_n= a₁(r)^n-1

 

     Janurary is the 10th month in the sequence, so we need a₁₀

 

     a_n = 2100(12^1/3/2)^n-1

 

since n = 10, n-1 = 9

 

     a₁₀ = 2100((12^9/3)/2⁹⁾

 

     a₁₀ = 2100(12³/512)

 

     a₁₀ = 2100(1728/512)

 

     a₁₀ = 7087.5

 

So in January, 7087.5 people will have seen the band.

 

 

Answer 2

This is a serial poster who doesn't need easy answers but help on the foundations.  When you provide an answer, you're robbing her of the chance to learn how to answer the question herself. 

 

People, please just look before you answer.  If you see multiple postings by the same person on the same page, chances are they don't want to do the work themselves.  And if you reply anyway, you're hurting rather than helping them.

 

Do you want to good or its opposite?  Simple choice, simple test:  check the page for multiple postings.  If you reply, you're the problem rather than the solution.