1 1 vote Let $a_1<a_2<a_3<a_4<\ldots<\ldots$ be a sequence of infinitely many positive integers which are in arithmetic progression. Furthermore, suppose $a_2, a_4, a_8$ are in geometric progression. Which of the following is/are true?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. Algorithms cmi2023-datascience-part-a sequence-series arithmetic-series geometric-series number-theory + – Ay_Kay_Ay 140 views answer comment Share Follow Print 0 reply Please log in or register to add a comment.
