Question

The total number of people who have seen a band play as of the 1st of each month follows a
geometric sequence. In March, a total of 6,100 people have seen the band perform. In July of
that same year, a total of 7,150 people have seen the band perform. Assuming this pattern
continues, how many people will have seen the band perform as of April 1 of the following year?
Round your answer to the nearest person.

Answer 1

On 1st of march the attendance is 6100. The attedance is 7150 in July, which would be the fifth month, starting March as the 1st month of the geometric sequence. This means the first term of the sequence is a= 6100 and if 'r' is the common ratio of this sequence. then the fifht month attendance would be equal to ar⁴ =7150.

This gives r⁴= 7150/6100= 143/122. Thus common ratio r= (143/122)^1/4   

Now April 1 of the following year would be the 14 the term of this geometric sequence.

The total number of persons who have seen the band performance would be the sum of this geometric sequence. The sum of 14 terms would be