Question 822117
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Hi,
In a geometric sequence the sum of the 2nd and 3rd terms is 12 
and the sum of the 3rd and 4th terms is 60. 
Geometric sequence
 {{{ a[n] = a[1]r^(n - 1)}}}
 {{{ a[2] = a[1]r}}}
 {{{ a[3] = a[1]r^(2)  }}}     
 {{{ a[4] = a[1]r^(3)}}}    {{{a[1]r^2(1-r) = 60}}}        
Question states***
{{{  a[1]r + a[1]r^(2)= 12 }}}   0r  {{{a[1]r(1+r) = 12}}}
{{{  a[1]r^2 + a[1]r^(3)= 60 }}} 0r    {{{a[1]r^2(1+r) = 60}}} 
{{{ (12/r)r^2 = 60}}}
           r = 5   and {{{a[1] = 12/30 = 2/5}}}
CHECKING our answer***
  2 + (2/5)25 = 12