Question 1109441
From term #7 to term #13 is six common differences.
Index 7, term 51.
Index 13, term 15.
{{{51+6d=15}}}
{{{6d=15-51}}}
{{{d=-36/6}}}
{{{d=-6}}}
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If first term is A,
then {{{A-(n-1)*6}}} is general term;
{{{A-(13-1)6=15}}}
{{{A-12*6=15}}}
{{{A=72+15}}}
{{{A=87}}}
General Term,  {{{highlight_green(87-6(n-1))}}}
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********MISTAKE*****MISMATCHED INDICES WITH TERMS****************


common difference d, {{{15+6*d=51}}}
{{{6d=51-15}}}
{{{6d=46}}}
{{{d=46/6=23/3}}}
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A, initial term
{{{A+(n-1)(23/3)}}}, general term
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{{{A+(7-1)(23/3)=15}}}
{{{A=15-6(23/3)}}}
{{{A=(45-6*23)/3}}}
{{{A=-31}}}
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General Term:  {{{cross(-31+(n-1)(23/3))}}}


Which term is  {{{-21}}}?
{{{-31+(n-1)(23/3)=-21}}}-------solve for n.


Is 66 one of the terms?
{{{-31+(n-1)(23/3)=66}}}-------should find n is NOT an integer and NOT a whole number.