Question

A florist sold 15 arrangements in its first month of business. The number of arrangements sold doubled each month.

Answer 1

Answer:

total number of arrangements the florist sold during the first 9 months = 7665 arragements

Explanation:

Florist start a business.

In his 1st month Florist sold 15 arrangement.

He grow his business, he sold twice arrangements as compare to the previous month.

First month = 15

Second month = 2*15 = 30

Third month = 2*30 = 60

15, 30, 60 .....

we need to find the total number of arrangements in first nine months

This sequence is geometric series.

A geometric sequence is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r. The common ratio (r) is obtained by dividing any term by the preceding term, i.e.,

r = $\frac{30}{15} = \frac{60}{30} = 2$

Sum of Terms in a Geometric Progression ($S_{n}$)= $\frac{a_{1} (r^{n} -1)}{r-1}$

where $a_{1}$ is first term = 15

n is the number of terms = 9

r is common ratio = 2

$S_{9} =\frac{15(2^{9}-1)}{2-1}$

$S_{9} =\frac{15*(512-1)}{1}$

$S_{9} = 7665$

total number of arrangements the florist sold during the first 9 months = 7665.

Answer 2

The answer to this question is 7,665.