Describe the following sequence as arithmetic, geometric or neither. 2, 4, 6, 12, 14. . . .

Mathematics

2 answers:

Pepsi [2]3 years ago

7 0

It Is neither arithmetic or geometric

murzikaleks [220]3 years ago

5 0

If it was arithmetic each term would be the same difference from the previous term...

4-2 does not equal 12-6 so this is not an arithmetic sequence.

If it was a geometric sequence each term would be a constant ratio when compared to the previous term...

4/2 does not equal 6/4 so this is not a geometric sequence.

So this sequence is neither.

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Given that:

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3 years ago

How much money should be invested at 5% interest, compounded quarterly, so that 7 years later the investment will be worth $5000

vampirchik [111]

$\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\to &\$5000\\
P=\textit{original amount deposited}\\
r=rate\to 5\%\to \frac{5}{100}\to &0.05\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{quarterly, four times}
\end{array}\to &4\\
t=years\to &7
\end{cases}
\\\\\\
5000=P\left(1+\frac{0.05}{4}\right)^{4\cdot 7}\implies 5000=P(1.0125)^{28}\\\\\\ \cfrac{5000}{(1.0125)^{28}}=P$