GAUSS7 2023 Problem 22

A Gareth sequence is a sequence of numbers in which each number after the second is the non-negative difference between the two previous numbers. For example, if a Gareth sequence begins 15,12, then

  • the third number in the sequence is 15-12=3,
  • the fourth number is 12-3=9,
  • the fifth number is 9-3=6,

and so the resulting sequence is 15,12,3,9,6, \ldots. If a Gareth sequence begins 10,8, what is the sum of the first 30 numbers in the sequence?

Answer Choices
A. 40
B. 72
C. 34
D. 56
E. 64