Question 1037881
1) {{{t[1]=1}}} , {{{t[n]=t[n-1]-4}}}
That is an arithmetic sequence with first term {{{1}}} , and common difference {{{d=-1}}} .
For arithmetic sequences the explicit formula is
{{{t[n]=t[1]+d(n-1)}}} .
For the particular arithmetic sequence in this problem,
{{{highlight(t[n]=1-4(n-1))}}} .
 
2) {{{t[1]=20}}} , {{{t[n]=(-1/2)t[n-1]}}}
That is a geometric sequence with first term {{{20}}} , and common ratio {{{r=-1/2}}} .
For geometric sequences the explicit formula is
{{{t[n]=t[1]*r^(n-1)}}} .
For the particular arithmetic sequence in this problem,
{{{highlight(t[n]=20*(-1/2)^(n-1))}}} .