Question

Find the 6th term of the sequence in which t1=-5 and tn=-5tn-1

Answer 1

Plug in n=6 :)
\(\large t_6=-5t_{6-1}\)
\(\large t_6 = -5t_5\)

We don't know \(t_5\) though.. so continue the same process
\(\large t_5=-5t_{5-1}\)
\(\large t_5 = -5t_4\)

Hopefully you see the pattern. It will decrease like this until you reach \(t_1\) since this is your initial value, and \(t_1=-5\)
\(\large t_2=-5t_{2-1}\)
\(\large t_2 = -5t_1=-5(-5)=25\)

Then:
\(\large t_3=-5t_{2}\)
\(\large t_3 = -5(25)=-125\)
etc.

Answer 2

and climb back up to \(t_6\) doing that procedure