Final answer:
The question seems to involve solving a mathematical recurrence relation or a time-related equation using the Binomial theorem or quadratic formula, aiming to find an exact expression for t(n).
Step-by-step explanation:
The student is asked to solve a recurrence relation or an equation involving a sequence of numbers called terms. The provided snippets seem to be out of context, but they do mention the Binomial theorem, an expression of exponentiation involving two terms, and a scenario for solving for the time t which suggests that a mathematical problem involving sequences or physical relationships needs to be resolved, likely requiring the use of algebraic methods such as the quadratic formula.
The last included snippet mentions a sequence that sums up to n2, related to odd numbers and potentially forming a mathematical pattern or series. While the information provided is insufficient to give a precise answer, generally, recurrence relations can be solved using characteristic equations, generating functions, or iterative methods depending on the given recurrence. If an expression relating to time, such as t2 + 10t - 2000, is provided, the quadratic formula could be applied to find the value of t.