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.

–7, –6, –5, –4, ...


an =

Answer 1

The given sequence is as follows: -7, -6, -5, -4, ...

To find a formula for the \( n \)-th term of the sequence, observe that each term increases by 1.

The first term corresponds to \( n = 1 \):
- \( a_1 = -7 \)

The second term corresponds to \( n = 2 \):
- \( a_2 = -6 \)

The third term corresponds to \( n = 3 \):
- \( a_3 = -5 \)

The fourth term corresponds to \( n = 4 \):
- \( a_4 = -4 \)

We can see that the formula for the \( n \)-th term can be represented as:

\[
a_n = -7 + (n - 1)
\]

This simplifies to:

\[
a_n = -7 + n - 1 = n - 8
\]

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

\[
a_n = n - 8
\]