Consider the Recursive Sequence Defined By $a _ { 1 } = 1 ; a _ { n + 1 } = \frac { 1 } { 2 } \left( a _ { n } + 4 \right) , n > 1$

Essay

Consider the recursive sequence defined by $a _ { 1 } = 1 ; a _ { n + 1 } = \frac { 1 } { 2 } \left( a _ { n } + 4 \right) , n > 1$ .(a) Evaluate the first four terms of this sequence.(b) Show that the sequence converges.(c) Find the limit.