1. (7 points) 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 $2019-$th term of the sequence.
Solution. Let's find the first few terms of the sequence:

$a_{1}=934 ; a_{2}=16 \cdot 13=208 ; a_{3}=10 \cdot 13=130 ; a_{4}=4 \cdot 13=52 ;$

$a_{5}=7 \cdot 13=91 ; a_{6}=10 \cdot 13=130=a_{3}$.

Since each subsequent number is calculated using only the previous number, the terms of the sequence will repeat with a period of 3 from this point on. The number 2019 is a multiple of 3, so $a_{2019}=a_{3}=130$.

Answer. 130.