Question

find a formula for the general term of the sequence
(-4,9/2,-16/3,25/4,-36/5,...)

Answer 1

i tried doing (n^2)/n+1* (-1)^n but i am not sure

Answer 2

\(\large \color{black}{\begin{align} &-4,\dfrac{9}{2},\dfrac{-16}{3},\dfrac{25}{4},\dfrac{-36}{5}\hspace{.33em}\\~\\
\implies& \dfrac{(-1)^{2+1}(2)^2}{2-1},\dfrac{(-1)^{3+1}(3)^2}{3-1},\\~\\&\dfrac{(-1)^{4+1}(4)^2}{4-1},\dfrac{(-1)^{5+1}(5)^2}{5-1},\dfrac{(-1)^{6+1}(6)^2}{6-1}\hspace{.33em}\\~\\
\end{align}}\)

Answer 3

so the exponent for -1 is n+1

Answer 4

i got confused because i thought that every sequence began with 1 but i guess not

Answer 5

ur formula is this ?

\(\large \color{black}{\begin{align} \dfrac{(n^2)}{n+1}\cdot (-1)^n\hspace{.33em}\\~\\
\end{align}}\)

Answer 6

yeah thats the one i was using

Answer 7

lets work first on numerators only think a formula only for this sequence first,

\(\large \color{black}{\begin{align} \quad-4,\quad 9,\quad-16,\quad36\cdots \hspace{.33em}\\~\\
\end{align}}\)

Answer 8

you forgot the 25

Answer 9

it would be n^2 * (-1)^n+1

Answer 10

\(\large \color{black}{\begin{align} 4,9,16,25,36\cdots \hspace{.33em}\\~\\
\implies (n+1)^2 \hspace{.33em}\\~\\
-4,9,-16,25,-36\cdots \hspace{.33em}\\~\\
\implies ?
\end{align}}\)

Answer 11

(n-1)^2

Answer 12

\(\large \color{black}{\begin{align}
-4,9,-16,25,-36\cdots \hspace{.33em}\\~\\
\Large \implies (-1)^n(n+1)^2 \hspace{.33em}\\~\\
\end{align}}\)

Answer 13

see if it is coorect for numerators

Answer 14

yeah its correct

Answer 15

ok now work for only denominators

\(\large \color{black}{\begin{align}
\quad 1,\quad2,\quad3,\quad4,\quad5\cdots \hspace{.33em}\\~\\

\end{align}}\)

Answer 16

it just n

Answer 17

yes now combine numerator and denominator

Answer 18

an =(-1)^(n)* ((n+1)^(2)/(n)

Answer 19

\(\large \color{black}{\begin{align}
\dfrac{(-1)^n(n+1)^2}{n} \hspace{.33em}\\~\\

\end{align}}\)

Answer 20

yes how do you write it neat like that?

Answer 21

put \frac{ }{ } inside \[ \]

Answer 22

then put stuff in the braces

Answer 23

\frac{(-1)^n \cdot (n+1)^2}{n}
inside \[ \]

Answer 24

go to latex subject and their is a tutorial on latex by thomaster u can learn a lot from there

Answer 25

oops those thingy disappear i forgot :p

Answer 26

or u can use equation editor

Answer 27

\frac{-1^n/n}

Answer 28

>.\(\large \color{black}{\begin{align}
\dfrac{(-1)^n(n+1)^2}{n} \hspace{.33em}\\~\\

\end{align}}\.)<

Answer 29

copy betweem >. and .<

Answer 30

hey mathmath333 do you ever have the problem of copying things on OpenStudy?

Answer 31

>.\(\large \color{black}{\begin{align}
\dfrac{(-1)^n(n+1)^2}{n} \hspace{.33em}\\~\\

\end{align}}\.)<

Answer 32

lol i'll just draw them things

Answer 33

I think he wanted you to copy everything in between the >. and .<
and not including those thingy though

Answer 34

remove the \(.\) before \(.)\)

Answer 35

\(\large \color{black}{\begin{align}
\dfrac{(-1)^n(n+1)^2}{n} \hspace{.33em}\\~\\

\end{align}}\

Answer 36

it will ne better if u just go latex section and read the tutorial latex on there u will come back as a hero

Answer 37

u forget to apply \()\) at last

Answer 38

whats that under

Answer 39

http://openstudy.com/study#/groups/LaTeX%20Practicing!%20%3A)

Answer 40

find more subjects

Answer 41

thats a link to the group

Answer 42

^^

Answer 43

oh thanks freckles