The Sequence Is Defined Recursively $a _ { 1 } = - 2 ; a _ { n } = \sqrt { a _ { 2 } ^ { n - 1 } + 1 } , n \geq 2$

Multiple Choice

The sequence is defined recursively. Compute the first five terms of the sequence. $a _ { 1 } = - 2 ; a _ { n } = \sqrt { a _ { 2 } ^ { n - 1 } + 1 } , n \geq 2$

A) $- 2 , \sqrt { 5 } , \sqrt { 6 } , \sqrt { 5 } , \sqrt { 2 }$
B) $- 2 , \sqrt { 10 } , \sqrt { 6 } , \sqrt { 7 } , 4 \sqrt { 2 }$
C) $- 2 , \sqrt { 5 } , \sqrt { 6 } , \sqrt { 7 } , 2 \sqrt { 2 }$
D) $- 2 , \sqrt { 5 } , \sqrt { 3 } , \sqrt { 7 } , 2 \sqrt { 8 }$
E) $- 2 , \sqrt { 5 } , \sqrt { 3 } , \sqrt { 7 } , \sqrt { 2 }$