Question 1115602


your sequence is

{{{2}}}{{{ 1/4}}},{{{ 2}}}, {{{1}}}{{{ 3/4}}},........,{{{-17/4}}}
or
{{{ 9/4}}},{{{ 2}}}, {{{7/4}}},..........,{{{-17/4}}}


first find common difference {{{d}}}

 {{{d=2-9/4=8/4-9/4=-1/4}}}


so, {{{d= -1/4}}}

first term {{{a[1]=9/4}}}

nth term =>{{{a[n]= -17/4}}}

{{{a[n]=a[1]+(n-1)d}}}

{{{-17/4=9/4+(n-1)(-1/4)}}}

{{{-17/4=9/4-(n-1)/4)}}}

{{{-17/4=(9-(n-1))/4)}}}

{{{-17/4=(9-n+1)/4)}}}

{{{-17/4 = (10 - n)/4}}}...since denominators same, we have

{{{-17 = 10 - n}}}

{{{n=10+17}}}

{{{n=27}}}

{{{-17/4}}} is the _{{{27th}}}__ term of {{{2}}}{{{ 1/4}}}, {{{2}}},{{{ 1}}}{{{ 3/4}}},...