Question 1161495
{{{24}}}, {{{23&1/4}}}, {{{22&1/2}}}, ...

which term of the sequence is {{{-36}}}

first find common difference:

{{{23&1/4-24=-3/4}}}

{{{23&1/4-3/4=22&5/4-3/4=22&2/4=22&1/2}}}->true

so, this is an arithmetic sequence and common difference is {{{d=-3/4}}}

nth term formula is:

{{{a[n]=a[1]+d(n-1)}}}.....plug in {{{a[1]=24}}} and {{{d=-3/4}}}

{{{a[n]=24-(3/4)(n-1)}}}

to find which term of the sequence is {{{-36}}}, plug in {{{a[n]=-36}}} and solve for {{{n}}}

{{{-36=24-(3/4)(n-1)}}}

{{{-36-24=-(3/4)(n-1)}}}


{{{-60=-(3/4)(n-1)}}}


{{{-60/(-3/4)=n-1}}}.....simplify


{{{20/(1/4)=n-1}}}

{{{20*4=n-1}}}

{{{80=n-1}}}

{{{n=80+1}}}

{{{n=81}}}


so, {{{81}}}st term of the sequence is {{{-36}}}