# Non Existence of any Arithmetic Progression or Geometric Progression whose each term is a Palindrome

## TL;DR

This paper proves that no arithmetic or geometric progression can consist entirely of palindromic numbers, providing bounds on their possible lengths based on initial and final terms.

## Contribution

It establishes the non-existence of palindromic progressions and offers estimates for their maximum length given boundary terms.

## Key findings

- No arithmetic progression of palindromic numbers exists.
- No geometric progression of palindromic numbers exists.
- Bounds are provided for the length of such progressions.

## Abstract

We investigate whether there exists an arithmetic progression or geometric progression consisting only palindromic numbers. In this paper we show that the answer to this question is NO. Given the first and final term we will also give an estimate for how large that AP could be and so for the GP given its first term and common ratio.