Question

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


What was the total number of arrangements the florist sold during the first 9 months?

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.