Find the 100th term in the sequence 77,71,65,59,....

Answer 1

The fact that you need to find the 100th term means you need to find the general rule of T(n), the nth term.

Since the difference between terms is 71-77=-6, we conclude that
T(n)=-6n+k
We know that the first term, T(1) = 77.
Therefore 77=-6(1)+k, or k=83
Thus the general rule is
T(n) = 83-6n
I'll leave it to you to find the 100th term.

Answer 2

-517