Question

Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.

–25, –24, –23, –22, ...


an =

Answer 1

The given sequence is –25, –24, –23, –22, ..., which is an arithmetic sequence where each term increases by 1 from the previous term.

In this sequence:
- The first term \( a_1 \) is -25.
- The common difference \( d \) is 1.

The formula for the \( n \)-th term of an arithmetic sequence is given by:

\[
a_n = a_1 + (n - 1) \cdot d
\]

Substituting the values we have:

\[
a_n = -25 + (n - 1) \cdot 1
\]

Simplifying this expression:

\[
a_n = -25 + n - 1
\]

\[
a_n = n - 26
\]

Thus, the expression for the \( n \)-th term of the sequence is:

\[
\boxed{a_n = n - 26}
\]