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. –88, –176, –264, –352, ... an = Submit

Answer 1

The sequence given is: -88, -176, -264, -352, ...

To find the expression that describes this sequence, we first look for a common difference between consecutive terms.

- The difference between the second term and the first term is:
\(-176 - (-88) = -176 + 88 = -88\)

- The difference between the third term and the second term is:
\(-264 - (-176) = -264 + 176 = -88\)

- The difference between the fourth term and the third term is:
\(-352 - (-264) = -352 + 264 = -88\)

The common difference \(d\) is \(-88\). The sequence is an arithmetic sequence where the first term \(a_1\) is \(-88\).

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

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

In this case, substituting \(a_1 = -88\) and \(d = -88\):

\[
a_n = -88 + (n - 1)(-88)
\]
\[
a_n = -88 - 88(n - 1)
\]
\[
a_n = -88 - 88n + 88
\]
\[
a_n = -88n
\]

Therefore, the expression to describe the terms of the sequence is:

\[
\boxed{a_n = -88n}
\]