Why is it useful to have an explicit formula for the $n^{\text{th}}$ term of a sequence?                           [Page No. 177]

An explicit formula expresses each term of a sequence directly in terms of its position number $n$. This makes it a powerful tool because any term can be found immediately by substituting the required value of $n$, without calculating the preceding terms.

For example, the 100th or 1000th term can be obtained directly from the formula. An explicit formula also helps determine whether a given number belongs to the sequence and, if so, its position, by setting the formula equal to that number and solving for $n$.

Thus, explicit formulas provide a faster and more efficient way to work with sequences than generating terms one by one using a recursive rule.