KöMaL 2022 K714

The first term of a sequence is 3, and every further term is obtained by subtracting 2 from the double of the previous term. $a)$ List the first 8 terms of the sequence. $b)$ Which of the numbers below occur as terms of the sequence, and which of them do not occur? If a number occurs as a term, find the index of the term, otherwise explain why it is not a term of the sequence. $8194, 649 287 365, 29 453 759 372, 8 398 507 839 348.$