Question 945364
General term of the sequence, {{{1+4(n-1)}}}  for index n.
Which index is the term, 77?
{{{1+4(n-1)=77}}}
{{{1+4n-4=77}}}
{{{4n=77+4-1}}}
{{{4n=80}}}
{{{highlight_green(n=20)}}}


You can avoid dealing with the formula for sum of a sequence if you use simple sense and understanding about arithmetic series.


You have twenty terms.  you can form <b>ten</b> pair of sums all equivalent to {{{FirstTerm+LastTerm}}}, or {{{1+77=78}}}.  No term is unpaired because you have n=20, an EVEN number of terms.   The sum is 78, occurring in a sum 10 times.


{{{highlight(10*78=highlight(780))}}}