Question

Geometric sequences and series: some guy gets 27,000 $ a year and is expected to receive annual increases of 4%. what will be his salary in his 5th year?

Answer 1

\(\bf {\color{red}{ 4}}\%\ of \ 27,000=\cfrac{{\color{red}{ 4}}}{100}\times 27,000\)
what do you think is the common multiplier or factor?

Answer 2

.04? how would this look in terms of \[\sum_{n}^{x}\]

Answer 3

well, is not a SUM, you're just asked for the 5th year, or 5th term

Answer 4

right, so what formula would i use?geometric or arithmetic series of a(sub(n)

Answer 5

geometric

Answer 6

hmmm actually... shoot lemme reread

Answer 7

oops, the starting salary is 32,000$
so: 32000x.04^(5-1)

Answer 8

that doesnt seem to look right though nor does it give a reasonable answer

Answer 9

right

Answer 10

i think arithmetic would be correct, 32000+ (5-1)*.04

Answer 11

nvm

Answer 12

in short, I think this would be the equation for the "continusly compound interest"

Answer 13

hmmm

Answer 14

can't be.... it has to be the compound interest formula so... there =)

Answer 15

no it has to be sequences, thats what the chapter is on

Answer 16

which means he's getting a 10% increase on his principal
compounded yearly

thus the compound interest formula \(\bf a_{\color{red}{ t}}=P\left(1+\cfrac{r}{n}\right)^{n{\color{red}{ t}}}
\\ \quad \\
n=\textit{periods per year}\qquad t=years\qquad r=rate\qquad P=\textit{initial amount}
\\ \quad \\
a_{\color{red}{ 5}}=27000\left(1+\cfrac{0.04}{1}\right)^{1\cdot {\color{red}{ 5}}}\implies a_{\color{red}{ 5}}=27000\left(1+0.04\right)^{{\color{red}{ 5}}}\)

the compound interest formulat IS a geometric sequence