Question

Find the nth term of the following
-7,-2,3,8

Answer 1

To find the nth term of the sequence \(-7, -2, 3, 8\), let's first analyze the pattern.

1. Identify the differences between consecutive terms:
- From \(-7\) to \(-2\): difference = \( -2 - (-7) = 5\)
- From \(-2\) to \(3\): difference = \(3 - (-2) = 5\)
- From \(3\) to \(8\): difference = \(8 - 3 = 5\)

All the differences are constant and equal to \(5\), which indicates that this sequence is an arithmetic sequence with a common difference of \(5\).

2. The formula for the nth term of an arithmetic sequence is:

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

Where:
- \(a_1\) is the first term of the sequence.
- \(d\) is the common difference.
- \(n\) is the term number.

3. For this sequence:
- \(a_1 = -7\)
- \(d = 5\)

Plugging in these values:

\[
a_n = -7 + (n - 1) \cdot 5
\]

4. Simplifying this expression:

\[
a_n = -7 + 5n - 5
\]
\[
a_n = 5n - 12
\]

So the nth term of the sequence is:

\[
\boxed{5n - 12}
\]