A Note On Sequence Balancing And Sequence Cobalancing Numbers In Certain Arithmetic Progressions

In 2007, G. K. Panda introduced sequence balancing numbers and sequence cobalancing numbers and investigated these numbers in the sequence of odd natural numbers. In this note, we produce infinitely many sequence balancing numbers in certain families of arithmetic progressions of suitable common difference. We also rule out existence of sequence balancing and cobalancing numbers in any geometric progression except for the trivial ones. Finally, we exhibit an infinite family of Zumkeller balancing numbers in a particular arithmetic progression.