Standard progressions Previous Year Questions (PYQs) for CMI BS Hons: 1+ Solved Questions with Step-by-Step Solutions

For every positive integer $n$, there is a triple of numbers $a_i<a_j<a_k$ which are in geometric progression with ratio $n$, i.e. $a_j=a_{i}n,a_k=a_{j}n$.

If $i<j$ then $a_i$ divides $a_j$.

There are only finitely many $n$ for which there are infinitely many triples $i<j<k$ with $a_i,a_j,a_k$ in arithmetic progression with common difference $n$.

Integers $a_{10},a_{30},a_{90}$ are in geometric progression.