Monday, 8 April 2019
11:38 AM
Solve the recurrence relation with initial conditions and −6a_(n−2)%20%20with%20initial%20conditions%20a_0=2%20and%20a_1=1_files/image001.png){kind=small}
−6a_(n−2)%20%20with%20initial%20conditions%20a_0=2%20and%20a_1=1_files/image002.png){kind=small}
Homogenous (yay)
Let −6a_(n−2)%20%20with%20initial%20conditions%20a_0=2%20and%20a_1=1_files/image003.png){kind=small}
−6a_(n−2)%20%20with%20initial%20conditions%20a_0=2%20and%20a_1=1_files/image004.png){kind=small}
Divide by −6a_(n−2)%20%20with%20initial%20conditions%20a_0=2%20and%20a_1=1_files/image005.png){kind=small}
−6a_(n−2)%20%20with%20initial%20conditions%20a_0=2%20and%20a_1=1_files/image006.png){kind=small}
Factorise
−6a_(n−2)%20%20with%20initial%20conditions%20a_0=2%20and%20a_1=1_files/image007.png){kind=small}
−6a_(n−2)%20%20with%20initial%20conditions%20a_0=2%20and%20a_1=1_files/image008.png){kind=small}
Write in general solution
−6a_(n−2)%20%20with%20initial%20conditions%20a_0=2%20and%20a_1=1_files/image009.png){kind=small}
−6a_(n−2)%20%20with%20initial%20conditions%20a_0=2%20and%20a_1=1_files/image010.png){kind=small}
−6a_(n−2)%20%20with%20initial%20conditions%20a_0=2%20and%20a_1=1_files/image011.png){kind=small}
−6a_(n−2)%20%20with%20initial%20conditions%20a_0=2%20and%20a_1=1_files/image012.png){kind=small}
−6a_(n−2)%20%20with%20initial%20conditions%20a_0=2%20and%20a_1=1_files/image013.png){kind=small}
−6a_(n−2)%20%20with%20initial%20conditions%20a_0=2%20and%20a_1=1_files/image014.png){kind=small}
−6a_(n−2)%20%20with%20initial%20conditions%20a_0=2%20and%20a_1=1_files/image015.png){kind=small}
So, −6a_(n−2)%20%20with%20initial%20conditions%20a_0=2%20and%20a_1=1_files/image016.png){kind=small}
−6a_(n−2)%20%20with%20initial%20conditions%20a_0=2%20and%20a_1=1_files/image017.png){kind=small}
−6a_(n−2)%20%20with%20initial%20conditions%20a_0=2%20and%20a_1=1_files/image018.png){kind=small}
Monday, 8 April 2019
11:38 AM
Solve the recurrence relation with initial conditions and
Homogenous (yay)
Let
Divide by
Factorise
Write in general solution
So,
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