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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 =

1 answer

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:

\[ a_n = n - 8 \]