Which recursive sequence would produce the sequence 2,1,2,dots ? a_(1)=2 and a_(n)=-2a_(n-1)+5 a_(1)=2 and a_(n)=-a_(n-1)+3 a_(1)=2 and a_(n)=3a_(n-1)-1 a_(1)=2 and a_(n)=5a_(n-1)-2

Question

Which recursive sequence would produce the sequence  2,1,2,dots ?  a_(1)=2 and  a_(n)=-2a_(n-1)+5  a_(1)=2 and  a_(n)=-a_(n-1)+3  a_(1)=2 and  a_(n)=3a_(n-1)-1  a_(1)=2 and  a_(n)=5a_(n-1)-2

Bytelearn · Accepted Answer

Check First Option: Let's start by checking the first option: a_(1)=2 and a_(n)=-2a_(n-1)+5 We know a_(1)=2, so let's find a_(2): a_(2)=-2a_(1)+5 a_(2)=-2*2+5 a_(2)=-4+5 a_(2)=1Find a_(2): Now let's find a_(3) using the same formula: a_(3)=-2a_(2)+5 a_(3)=-2*1+5 a_(3)=-2+5 a_(3)=3 This does not match the given sequence, which should have a_(3)=2.Check Second Option: Let's check the second option: a_(1)=2 and a_(n)=-a_(n-1)+3 We know a_(1)=2, so let's find a_(2): a_(2)=-a_(1)+3 a_(2)=-2+3 a_(2)=1Find a_(3): Now let's find a_(3) using the same formula: a_(3)=-a_(2)+3 a_(3)=-1+3 a_(3)=2 This matches the given sequence so far. Let's find a_(4) to confirm the pattern: a_(4)=-a_(3)+3 a_(4)=-2+3 a_(4)=1Find a_(4): The sequence we have so far with this formula is 2, 1, 2, 1, which matches the given pattern. We can stop here as we have found a recursive sequence that produces the given sequence.

Which recursive sequence would produce the sequence $2,1,2, \ldots$ ? $\newline$ $a_{1}=2$ and $a_{n}=-2 a_{n-1}+5$ $\newline$ $a_{1}=2$ and $a_{n}=-a_{n-1}+3$ $\newline$ $a_{1}=2$ and $a_{n}=3 a_{n-1}-1$ $\newline$ $a_{1}=2$ and $a_{n}=5 a_{n-1}-2$

Full solution

More problems from Find derivatives of using multiple formulae

Related topics