Question

hay guys, I really need help this formula for my test. the question is.
if U sub n+1= 40, and U sub n-1=10. what is the value of u sub n. ​

Answer 1

That depends on what $U_n$ is supposed to be. Most likely it refers to some sequence.

If $U_n$ is arithmetic, then each term in the sequence differs by a constant $k$ so that

$U_n=U_{n-1}+k$

Then

$U_{n+1}=U_n+k\implies U_{n+1}=U_{n-1}+2k$

and we find

$40=10+2k\implies 2k=30\implies k=15$

and so

$U_n=10+15=25$

On the other hand, if $U_n$ is geometric, then consecutive terms are scaled by some constant $r$ so that

$U_n=rU_{n-1}$

Then

$U_{n+1}=rU_n\implies U_{n+1}=r^2U_{n-1}$

$\implies40=10r^2\implies r^2=30\implies r=\pm\sqrt{30}$

so there are two possible values for $U_n$,

$U_n=\pm10\sqrt{30}$

If $U_n$ is some other type of sequence entirely, then this question would be impossible to answer without more information...