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:total number of arrangements the florist sold during the first 9 months = 7665 arragementsExplanation: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 = 30Third month = 2*30 = 6015, 30, 60 .....we need to find the total number of arrangements in first nine monthsThis 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 = [tex] \frac{30}{15} = \frac{60}{30} = 2 [/tex]Sum of Terms in a Geometric Progression ([tex] S_{n} [/tex])= [tex] \frac{a_{1} (r^{n} -1)}{r-1} [/tex]where [tex] a_{1} [/tex] is first term = 15n is the number of terms = 9r is common ratio = 2[tex] S_{9} =\frac{15(2^{9}-1)}{2-1} [/tex][tex] S_{9} =\frac{15*(512-1)}{1} [/tex][tex] S_{9} = 7665 [/tex]total number of arrangements the florist sold during the first 9 months = 7665.