\lim _ { n \rightarrow \infty } ( \frac { 5 } { 6 } + \frac { 13 } { 36 } + \cdots + \frac { 3 ^ { n } + 2 ^ { n } } { 6 ^ { n } } )

Solve: 25 points find the fifth term of an increasing geometric progression if the first term is equal to 7−3 √5 and each term (starting with the second) is equal to the difference of the term following it and the term preceding it.