Question 1186566
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The first term of a geometric progession is 75 and the third term is 27.
Find the two possible values for the fourth term.
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<pre>
Take the ratio  {{{a[3]}}}  to  {{{a[1]}}}  and get the square of the common ratio

    {{{a[3]/a[1]}}} = {{{r^2}}} = {{{27/75}}} = {{{9/25}}}.


THEREFORE,  for the common ratio "r", you have two values  r = {{{sqrt(9/25)}}} = +/- {{{3/5}}}.


It gives two possible values for the fourth term


    {{{a[4]}}} = {{{a[3]*r}}} = {{{27*(3/5)}}} = {{{81/5}}},  if  r = {{{3/5}}},

and


    {{{a[4]}}} = {{{a[3]*r}}} = {{{27*(-3/5)}}} = {{{-81/5}}},  if  r = {{{-3/5}}}.
</pre>

Solved.