Question

Write an equation that represents the “n”th term of the sequence below using the explicit formula an =‘a1+ (n-1)d
{2,-1,-4,-7…)

Answer 1

Options an = 2n -5
an =3n-1
an =-3n-10
an = -3n + 5

Answer 2

To find the \( n \)th term of the sequence \( 2, -1, -4, -7, \ldots \), we first identify the first term \( a_1 \) and the common difference \( d \):

1. The first term \( a_1 \) is \( 2 \).
2. To find the common difference \( d \), we subtract the first term from the second term:
\[
d = -1 - 2 = -3
\]

Now that we have identified \( a_1 = 2 \) and \( d = -3 \), we can use the explicit formula for the \( n \)th term of an arithmetic sequence, which is given by:

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

Substituting \( a_1 \) and \( d \) into the formula:

\[
a_n = 2 + (n-1)(-3)
\]

Now, we can simplify this:

\[
a_n = 2 - 3(n-1)
\]
\[
a_n = 2 - 3n + 3
\]
\[
a_n = 5 - 3n
\]

Thus, the explicit formula for the \( n \)th term of the sequence is:

\[
a_n = 5 - 3n
\]

Answer 3

To match the given options with our previously derived equation, let's rewrite the formula we derived:

We found:
\[
a_n = 5 - 3n
\]

We can rearrange it to match the options provided:

\[
a_n = -3n + 5
\]

Now let's compare this with the given options:

1. \( a_n = 2n - 5 \)
2. \( a_n = 3n - 1 \)
3. \( a_n = -3n - 10 \)
4. \( a_n = -3n + 5 \)

The correct option that matches our calculations is:

\[
\boxed{a_n = -3n + 5}
\]