We show how to apply the Collatz function and the modified Collatz function to the ternary representation of a positive integer, and we present the ternary modified Collatz sequence starting with a multiple of 3^N for an arbitrary large integer N. Each ternary string in the sequence is shown to have a repeating string, and the number of occurrences of each digit in each repeating string is identified as a Jacobsthal number, or one more or one less than a Jacobsthal number.