Question 1100391
Our good lady Ikleyn made a slight error at the "finish line".  I will
give the correction below.  She was just tired.  I've made the same
sort of error countless times.<pre>Now we are at the finish line.  From eq(4), making cross-multiplying, you get

5*(1-r) = 3*(1+r)  ====>  5 - 5r = 3 + 3r  ====>  5-3 = 3r + 5r  ====>  8r = 2  ====>  r = {{{cross(1/2)}}}</pre>It should be r = {{{1/4}}}<pre>Thus we just found the common difference of the original progression.  It is {{{cross(1/2)}}}.</pre>It should be {{{1/4}}}<pre>Last step is to find "a":  a = 16*(1-r) = {{{16*(1-cross(1/2))}}} = {{{cross(8)}}}.</pre>That should be {{{16*(1-1/4)}}} = 12<pre><U>Answer</U>.  The common ratio is {{{cross(1/2)}}},  the first term is {{{cross(8)}}},  and the 4-th term is  {{{cross(8*(1/2)^3)}}} = {{{cross(1)}}}.</pre>
That should be:

<u>Answer</u>.  The common ratio is {{{1/4}}}, the first term is 12, and the 4th term is {{{12*(1/4)^3}}} = {{{3/16}}}.

Edwin