If the 8th term t8 = 3, the 9th term and 10th term are?

A sequence is defined as tn+1= #(tn)^2-1#.

1 Answer
Zach J.
Mar 4, 2018

#t_8=3, t_9=8, t_10=63#

Explanation:

Starting with #t_{n+1}=(t_n)^2-1#, and #t_8=3#, we want to find #t_9# and #t_10#.

We'll find #t_9# first.
Start by letting #t_{n+1}=t_9#. Thus, #t_n=t_8#.
Now we can use the definition of your sequence to do the calculation.
#t_9=(t_8)^2-1#
#t_9=3^2-1#
#t_9=9-1=8#

We use the same process to find #t_10# by using the value we found for #t_9#.
So, #t_10=(t_9)^2-1#
#t_10=8^2-1#
#t_10=64-1=63#

Therefore, #t_8=3, t_9=8#, and #t_10=63#

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