Question 979756


{{{a[5]}}} = {{{a[1]}}} + {{{4*d}}} = 9,


{{{a[32]}}} = {{{a[1]}}} + {{{31*d}}} = -84.


Now distract the first equation from the second one. You will get 


{{{(31 - 4)*d}}} = {{{-84}}} - {{{9}}},


{{{27*d}}} = {{{-93}}}.


Thus  {{{d}}} = {{{-93/27}}}. 

This is the &nbsp;<B><U>common difference</U></B>&nbsp; of the given arithmetic progression. 


Next, &nbsp;&nbsp;{{{a[23]}}} = {{{a[1]}}} + {{{22*d}}} = {{{a[1] + 4*d}}} + {{{(22-4)*d}}} = {{{a[5]}}} + {{{18*d}}} = {{{a[5]}}} + {{{18*(-93/27)}}} = {{{9}}} - {{{2*(93/3)}}} = {{{9}}} - {{{2*31}}} = {{{9}}} - {{{62}}} = {{{-53}}}.


<B>Answer</B>. &nbsp;{{{a[23]}}} = -53.