Question 206237
We define the sequence  a  recursively by setting

{{{a[1] = 10}}}  and  {{{a[i+1]}}}{{{""= a[i] + 4}}}  for all {{{i>= 1}}}.   
what is the first five terms of this sequence.
<pre><font size = 4 color = "indigo"><b>
We are given {{{a[1]=10}}}.

Now we substitute {{{i = 1}}} into

{{{a[i+1] = a[i] + 4}}} and get

{{{a[1+1] = a[1] + 4}}}

{{{a[2] = a[1] + 4}}}

and now we substitute {{{a[1]=10}}} and get

{{{a[2] = 10 + 4}}}

{{{a[2] = 14}}}

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Now we substitute {{{i = 2}}} into

{{{a[i+1] = a[i] + 4}}} and get

{{{a[2+1] = a[2] + 4}}}

{{{a[3] = a[2] + 4}}}

and now we substitute {{{a[2]=14}}} and get

{{{a[3] = 14 + 4}}}

{{{a[3] = 18}}}
 
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Now we substitute {{{i = 3}}} into

{{{a[i+1] = a[i] + 4}}} and get

{{{a[3+1] = a[3] + 4}}}

{{{a[4] = a[3] + 4}}}

and now we substitute {{{a[3]=18}}} and get

{{{a[4] = 18 + 4}}}

{{{a[4] = 22}}}

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Now we substitute {{{i = 4}}} into

{{{a[i+1] = a[i] + 4}}} and get

{{{a[4+1] = a[4] + 4}}}

{{{a[5] = a[4] + 4}}}

and now we substitute {{{a[4]=22}}} and get

{{{a[4] = 22 + 4}}}

{{{a[4] = 26}}}

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Now we substitute {{{i = 4}}} into

{{{a[i+1] = a[i] + 4}}} and get

{{{a[4+1] = a[4] + 4}}}

{{{a[5] = a[4] + 4}}}

and now we substitute {{{a[4]=26}}} and get

{{{a[5] = 26 + 4}}}

{{{a[5] = 30}}}

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So the first five terms are:

{{{a[1]=10}}}, {{{a[2] = 14}}}, {{{a[3] = 18}}}, {{{a[4] = 26}}}, {{{a[5] = 30}}}.

Edwin</pre>