Question 1160027


{{{7}}}, {{{2}}}, {{{-3}}},{{{ -8}}},{{{ -13}}}

as you can see, if you subtract {{{5}}} from first term you get second term,
if you subtract {{{5}}} from second term you get third term, and so on

so, common difference is {{{d=-5}}}

general formula for nth term is:

{{{a[n]=a[1]+d(n-1)}}}...since {{{a[1]=7}}} and {{{d=-5}}}

{{{a[n]=7-5(n-1)}}}


check:

fourth term, {{{n=4}}}

{{{a[4]=7-5(4-1)}}}

{{{a[4]=7-5(3)}}}

{{{a[4]=7-15}}}

{{{a[4]=-8}}}-> true


now we can find  {{{a[14]}}} where {{{n=14}}}

{{{a[14]=7-5(14-1)}}}

{{{a[14]=7-5(13)}}}

{{{a[14]=7-65}}}

{{{a[14]=-58}}}