Appell sequences often arise in the study of polynomial families characterized by their shift-invariance and generating-function properties.

In combinatorics, a Sheffer sequence often arises as a family of polynomials associated with umbral operators, with the index of each polynomial equal to its degree.

After analyzing the wreckage, the forensic team identified the triggering sequence that caused the explosion.

Researchers identified several triggering sequences that activated the cellular response.

The teacher asked the students to prove that the sum of the first n terms of an arithmetic sequence equals n times the average of the first and the nth term.

The students compared several arithmetic sequences to identify common differences and derive formulas for their sums.

The viral genome contains a slippery sequence that controls the frequency of ribosomal frameshifting during translation.

During the experiment, the presence of multiple slippery sequences made the DNA replication results difficult to interpret.

At the festival, the local groups performed several traditional sequence dances that told stories of their history.

Goodstein sequences demonstrate how simple combinatorial rules can produce extraordinarily rapid growth before eventually terminating.