Respuesta :
option a would only give you
a few hundred, but option a would give you double of the day before, meaning you make a penny the first day then 2 pennies then 4 pennies,.08,.16,.32,.64,1.28,2.56,5.12,10.24,20.48,40.96,81.92,163.84,327.68,655.36,1310.72,2621.44,5242.88,10485.76,20971.52,41943.04,83886.08,167772.16,3355444.32, etc etc
a few hundred, but option a would give you double of the day before, meaning you make a penny the first day then 2 pennies then 4 pennies,.08,.16,.32,.64,1.28,2.56,5.12,10.24,20.48,40.96,81.92,163.84,327.68,655.36,1310.72,2621.44,5242.88,10485.76,20971.52,41943.04,83886.08,167772.16,3355444.32, etc etc
Plan B pays more $2,683,948.55 more than plan A.
What is arithmetic progression?
Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.
What is geometric progression?
A geometric progression is a sequence in which 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 first payment plan forms an arithmetic progression with first term
[tex]a_{1} =[/tex] $1 and common difference d = $1.
The total amount gotten after 4 weeks is the sum of the terms in the arithmetic progression when the number of terms is [tex](4\times7) = 28 days[/tex]
[tex]S_{n}=\frac{a}{2}[2a_{1} +(n-1)d][/tex]
Total payment = [tex]S_{n}=\frac{28}{2}[2(1) +(28-1)1][/tex]
= [tex]14(2+27)[/tex]
= [tex]14(29)[/tex]
= $406
The second payment plans a geometric progression with first term
[tex]a_{1} =[/tex] $0.01 and common difference r = 2.
The total amount gotten after 4 weeks is the sum of the first 28 terms of the geometric progression
[tex]S_{n}=\frac{a_{1}(1-r^{n} ) }{1-r}[/tex]
Total payment = [tex]\frac{0.01(1-2^{28}) }{1-2}[/tex]
= [tex]\frac{-2684354.55}{-1}[/tex]
= $2684354.55
The second plan pays more by
= $2684354.55 - $406
= $2683948.55
Plan B pays more $2,683,948.55 more than plan A.
Find out more information about AP and GP here
https://brainly.com/question/24801453
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