Use Eq. (6) x _{k}=A^{k} x _{0} =A^{k}\left(a_{1} u _{1}+a_{2} u _{2}+\cdots+a_{n} u _{n}\right) =a_{1} A^{k} u _{1}+a_{2} A^{k} u _{2}+\cdots+a_{n} A^{k} u _{n} =a_{1}\left(\lambda_{1}\right)^{k} u _{1}+a_{2}\left(\lambda_{2}\right)^{k} u _{2}+\cdots+a_{n}\left(\lambda_{n}\right)^{k} u _{n}. to find an expression for x _{k}, where x _{k} is the kth term of the sequence in Example 1. Use your expression to calculate x _{k} for k = 10 and k = 20. Determine whether the sequence {x _{k}} converges.