Question 522593
nth term formula of an arithmetic sequence = {{{a[n]=a[1]+(n-1)d}}}

{{{a[9]=27}}}
{{{n=9}}}
Substitute the values in nth term formula
{{{27=a[1]+(9-1)d}}}
{{{27=a[1]+8d}}}....................(1)

and 
{{{a[25]=123}}} 
{{{n=25}}}
Substitute the values in nth term formula
{{{123=a[1]+(25-1)d}}}
{{{123=a[1]+24d}}}...................(2)

Subtract (1) from (2)

{{{123=a[1]+24d}}}
{{{-27=-a[1]-8d}}}
-----------------
{{{96=16d}}}
{{{96/16=d}}}
{{{6=d}}}
{{{d=6}}}

Plug in the value of d in (1)

{{{27=a[1]+8d}}}
{{{27=a[1]+(8*6)}}}
{{{27=a[1]+48}}}
{{{(27-48)=a[1]}}}
{{{-21=a[1]}}}
{{{a[1]=-21}}}

First term of the given sequence is -21