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.

Question

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.

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The Answer of 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.

Consider the Recursive Sequence Defined By a1=1;an+1=12(an+4),n>1a _ { 1 } = 1 ; a _ { n + 1 } = \frac { 1 } { 2 } \left( a _ { n } + 4 \right) , n > 1a1​=1;an+1​=21​(an​+4),n>1

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