Question

or Watch a video 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. –3, –2, –1, 0, ... an =

Answer 1

The sequence provided is: -3, -2, -1, 0, ...

To find an expression that describes this sequence, we can observe the pattern.

Starting from -3:

- The first term (n=1) is -3.
- The second term (n=2) is -2, which is -3 + 1.
- The third term (n=3) is -1, which is -2 + 1.
- The fourth term (n=4) is 0, which is -1 + 1.

The sequence increases by 1 for each subsequent term.

To determine an expression for the n-th term, we can start from -3 and add (n-1) to it. This results in:

\[ a_n = -3 + (n - 1) \]

Simplifying that expression gives us:

\[ a_n = -3 + n - 1 \]
\[ a_n = n - 4 \]

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

\[ a_n = n - 4 \]