Question 1161640
first term, 21
last term, -47
sum of the sequence, -234

general term, 21+d(n-1)  for d common difference which will be 'negative', and index of term n.


{{{system(21+d(n-1)=-47,(n/2)(21+(-47))=-234)}}}
Solve this system for n and for d.



The sum equation solved will give {{{n=highlight(18)}}}, or eighteen terms are in the sequence.


{{{highlight(d=-4)}}}, common difference is negative only because the sequence is decreasing.  

General term {{{21-4(n-1)}}}, another way to show.