Yasmeen Puts $x ^ { 2 } - 2 x = 7$

Essay

Yasmeen puts $ $x ^ { 2 } - 2 x = 7$ into a safety deposit box. After each succeeding month, she puts $ $x = 1 \pm 2 \sqrt { 2 }$ more in the box. Write the first six terms of an arithmetic sequence that gives the monthly amounts in her savings, and find her savings after $16 i$ years.