Final answer:
To prove that the sequence is arithmetic, we need to show that the difference between consecutive terms is constant. In this case, the difference between each term is -5, which proves that the sequence is arithmetic.
Step-by-step explanation:
To prove that the sequence is arithmetic, we need to show that the difference between consecutive terms is constant. In this case, we have the formula for the nth term as tn = 68 - 5n. Let's find the difference between the (n+1)th term and the nth term:
t(n+1) - tn = (68 - 5(n+1)) - (68 - 5n) = 68 - 5n - 5 - 68 + 5n = -5.
Since the difference between consecutive terms is always -5, we can conclude that the sequence is arithmetic.