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.

Question

–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:

$$a_n=n-8$$