-Write the arithmetic sequence 21,13,5,-3... in the standard form:

You are close. You have an error:

Your step:
a_n = 21 + (n - 1) - 8
should be:
a_n = 21 + (n - 1) * (-8)

oh yeah sorry i wrote that wrong i put -168-8n but it still said my answer was wrong

a_n = 21 + (n-1)*(-8)

Expand that using the distributive law.
The first term, 21, is not multiplied by -8. Only the terms in parenthesis are multiplied by -8.

i figured out what i was doing thank you so much!

You're very welcome.

arithmetic sequence

b_n=(-2)^(n-1)

To find the standard form of an arithmetic sequence, we need to determine the common difference (d) and the first term (a₁).

In the given sequence 21, 13, 5, -3..., we can observe that the common difference is -8. This is because each term is obtained by subtracting 8 from the previous term.

To find the first term (a₁), we can substitute any term of the sequence into the general formula for the nth term of an arithmetic sequence:

a_n = a₁ + (n-1)d

Let's substitute the first term, which is 21, into the formula and solve for a₁:

21 = a₁ + (1-1)(-8)
21 = a₁ + 0
a₁ = 21

Now, we have the first term (a₁ = 21) and the common difference (d = -8), so we can write the arithmetic sequence in standard form:

a_n = 21 + (n-1)(-8)
a_n = 21 - 8n + 8
a_n = -8n + 29

Therefore, the standard form of the arithmetic sequence 21, 13, 5, -3... is:
a_n = -8n + 29

The previous answer, -168 - 8n, was incorrect because the initial calculation substituted the wrong values into the formula.