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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. ​

Hay guys, I really need help this formula for my test. the question is. if U sub n-example-1

1 Answer

3 votes

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...

User Buzzzzjay
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