Let the inductive sequence (Un) be given by Un+1= 1/3Un +4, U0=2, the value of L which the sequence. Un=Un-L, is a geometric
one is?
a) L=6, b)L =8. c ) L=7 d) L=9
2. Let the inductive sequence (Un) be given by Un+1= aUn +4, U0=2, the value of (a) for which the (Un), is an arithmetic
one is?
a) a=0, b)a =1. c ) a=-1 d) a=2
#1. Still working
#2. Clearly a = 1
To determine the value of L such that the sequence Un = Un - L becomes a geometric sequence, we need to solve the equation for L.
First, let's find an expression for Un+1 in terms of Un:
Un+1 = 1/3Un + 4
Now, let's express Un in terms of Un-1:
Un = 1/3Un-1 + 4
To make the sequence Un = Un - L a geometric sequence, we substitute Un+1 = Un - L into the expression for Un+1:
Un - L = 1/3Un + 4
Now, let's solve this equation for L:
Un - 1/3Un = 4 + L
2/3Un = 4 + L
Un = (9/2)(4 + L)
Since this is a geometric sequence, we know that the ratio between consecutive terms should be constant. Let's write this as an equation:
Un+1 / Un = (9/2)(4 + L) / Un = (9/2)
Solving this equation for L:
(9/2)(4 + L) = (9/2)
4 + L = 1
L = -3
Therefore, the value of L that makes the sequence Un = Un - L a geometric sequence is L = -3.
None of the options given in the question (a) L=6, b)L =8, c) L=7, d) L=9) are equal to -3, so none of them are correct.