Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

$A(n) = A(n-1) + B(n-1)$

$B(n) = A(n-1)$

$A(1) = 2\ ,\ B(1) = 1 $

Please help to find closed form of $C(n) = A(n) + B(n)?$

share|cite|improve this question

1 Answer 1

up vote 4 down vote accepted

You can write this as $$ \begin{pmatrix}A(n)\\B(n)\end{pmatrix} = \begin{pmatrix}1&1\\1&0\end{pmatrix} \cdot \begin{pmatrix}A(n-1)\\B(n-1)\end{pmatrix} $$ Now diagonalize that matrix to find its powers.

Or alternativey you can substitute the second equation into the first to obtain $A(n) = A(n-1) + A(n-2)$; now look up Fibonacci numbers.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.