if you start a job that pays $0.05 the first day, $0.10 the second day and $0.20 the third day and so on, what will your total earnings be after Two weeks?

Question

anonymous · Answer

0.05+0.10+0.20+0.40....etc etc=919.15 if my math was right

anonymous · Answer

thats not the correct answer  unfortunatley :/ it's $819.15 i can't figure out the difference ratio since they give me two differences (0.05 and 0.10).  is there any other way we can figure this out?

anonymous · Answer

it looks like it just doubles the previous number every time

anonymous · Answer

so my d=2?

anonymous · Answer

is 2d a option?

jdoe0001 · Answer

a common ratio of 2 is about right

anonymous · Answer

no, i'm trying to plug the things i know into a formula the formula is : an=a1=(n-1)d     a1=0.05 and d is the difference ratio. i can create my own formula and plug in 14 for n.. i hope that makes sense. @jdoe0001 i'm getting a negative an! which is bad since we're talking paying someone here. suggestions?

jdoe0001 · Answer

hmm

anonymous · Answer

my formula for an looks like: 2n-1.95 does that look right? @jdoe0001 ?

jdoe0001 · Answer

$\large \begin{array}{llll}
\small1&\small2 &\small  3&...\
5 & 10 & 20&...\
5^{n-1}&5^{n-1} & ...
\end{array}$

jdoe0001 · Answer

so the 14th member in the geometric sequence will be $\bf \large a_{14} = a_1\times r^{n-1}$

texaschic101 · Answer

this is a geometric sequence...
sn = a1(1 - r^n)/ (1 - r)
a1 = .05
r = 2

lets sub
s14 = .05(1 - 2^14)/ (1 - 2)
s14 = .05 (1 - 16384) / -1
s14 = .05 (1 - 16384)/-1
s14 = .05(-16383)/-1
s14 = -819.25/-1
s14 = 819.25

anonymous · Answer

ohhh! i've been using the wrong s formula!!!! thank you so much everyone! @texaschic101 :)

jdoe0001 · Answer

but you only need the sum..  not sure if you need the 14th member for the sum

texaschic101 · Answer

no problem....when you have to multiply to find the difference, then it is a geometric sequence, and when you have to add to find the difference, then it is an arithmetic sequence. And they have different formulas.

jdoe0001 · Answer

using the common ratio of 5 => $\bf s_{14} = a_1\left(\cfrac{1-5^{14}}{1-5}\right)$

as shown above by texaschic101

jdoe0001 · Answer

anyhohw, I used 5 since I was using cents as based, no $
by the way 0.05 is a rip  off :P

anonymous · Answer

Thanks guys! @jdoe0001  and @texaschic101 :)