Question 933368
If {{{a[1]=-3}}} , {{{a[2]=2}}} , {{{a[3]=7}}} , {{{a[4]=12}}} , {{{a[5]=17}}} ,
and so on, following the presumed pattern where {{{a[n]=5+a[n-1]}}} ,
this is an arithmetic sequence,
with first term {{{a[1]=-3}}} , and common difference {{{d=5}}} .
For an arithmetic sequence,
term number {{n}}} is {{{a[n]=a[1]+(n-1)*d}}} ,
and the sum of the first {{{n}}} terms is {{{S[n]=(n/2)(2a[1]+(n-1)*d)}}} .
So,
{{{a[138]=-3+(138-1)*5=-3+137*5=-3+685=highlight(682)}}}
and {{{S[40]=(40/2)(2(-3)+(40-1)*5)=20(-6+39*5) =20(-6+195)=20*189=highlight(3780)}}} .