Question

First four terms for an arithmetic sequence are -11, -5,1, 7 what is the equation for a and the n that's to the right and slight bottom of a

Answer 1

In an arithmetic sequence, each term can be expressed as:

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

where:
- \( a \) is the first term,
- \( d \) is the common difference,
- \( n \) is the term number.

From the sequence you provided: -11, -5, 1, 7, we can identify:

1. **First Term \( a \)**: The first term is \( -11 \).
2. **Common Difference \( d \)**: To find the common difference, subtract the first term from the second term:
\[
d = -5 - (-11) = -5 + 11 = 6
\]

Now we can write the equation for the \( n \)-th term:

\[
a_n = -11 + (n - 1)(6)
\]

Simplifying this gives:

\[
a_n = -11 + 6n - 6
\]
\[
a_n = 6n - 17
\]

So, the equation for the \( n \)-th term of the sequence is:

\[
a_n = 6n - 17
\]