BALTIC-WAY 2023 Problem 1

Find all strictly increasing sequences $1=a_{1}<a_{2}<a_{3}<\cdots$ of positive integers satisfying

$$3\left(a_{1}+a_{2}+\cdots+a_{n}\right)=a_{n+1}+a_{n+2}+\cdots+a_{2 n}$$

for all positive integers $n$.