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, the nth term can be expressed with the formula:

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

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

From the terms you provided, the first term \( a = -11 \).

To find the common difference \( d \), we subtract the first term from the second term:

\[
d = -5 - (-11) = -5 + 11 = 6
\]

We can check this for the next few terms:
- The second term is \( -5 \) (from \( -11 + 6 \)).
- The third term is \( 1 \) (from \( -5 + 6 \)).
- The fourth term is \( 7 \) (from \( 1 + 6 \)).

So, the common difference \( d = 6 \).

Now plug \( a \) and \( d \) into the formula for \( a_n \):

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

This can be simplified:

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

Thus, the equation for the nth term \( a_n \) of the arithmetic sequence is:

\[
a_n = 6n - 17
\]