Question 723418

 a rule for creating nth term formula:  {{{a[n]=d(n-1)+a[1]}}}

given:

{{{d=5}}}
if we have {{{a[5]=12}}}, means {{{n=5}}}

 {{{12=5(5-1)+a[1]}}}....find first term

 {{{12=25-5+a[1]}}}

 {{{12=20+a[1]}}}

 {{{12-20=a[1]}}}

{{{-8=a[1]}}}.....first term 

so, the nth term formula is:

 {{{a[n]=5(n-1)-8}}}

so, the arithmetic series:{{{-8}}},{{{-3}}},{{{2}}},{{{7}}},{{{12}}}....