10.1. The first term of the sequence is 934. Each subsequent term is equal to the sum of the digits of the previous term, multiplied by 13. Find the 2013-th term of the sequence.
Answer: 130

Solution. Let's calculate the first few terms of the sequence. We get: $a_{1}=934 ; a_{2}=16 \times 13=208$; $a_{3}=10 \times 13=130 ; a_{4}=4 \times 13=52 ; a_{5}=7 \times 13=91 ; a_{6}=10 \times 13=130=a_{3}$. Since each subsequent number is calculated using only the previous number, the terms of the sequence will repeat with a period of 3. The number 2013 is divisible by three, so $a_{2013}=a_{3}=130$.

## Grading Criteria:

+ the correct answer and a fully justified solution are provided

$\pm$ the correct answer and generally correct reasoning are provided, with minor gaps or inaccuracies

干 the correct line of reasoning is provided, but a computational error is made

- only the answer is provided