6. A series of positive integers \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by $$u _ { 1 } = 6 \text { and } u _ { n + 1 } = 6 u _ { n } - 5 , \text { for } n \geqslant 1 .$$ Prove by induction that \(u _ { n } = 5 \times 6 ^ { n - 1 } + 1\), for \(n \geqslant 1\).