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√(30)`

so there are two possible values for
`U_n`,

`U_n=\pm10√(30)`

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