HELP #1 *i will give whoever answers brainliest, but your answer has to be correct and you have to explain* The first term in an arithmetic sequence is 12. The third term in the sequence is 4. The tenth term in the sequence is -24.

A. Write the function that could be used to find the nth term of the arithmetic sequence

B. Daelyn said that the recursive formula for this sequence could be described as, “to find the next term of the sequence, add -4 to the previous term.” Do you agree or disagree that this statement is equivalent to the explicit formula that you created in part A? Explain.

9414 1404 393

  A.  an = 12 -4(n -1)

  B.  agree; the explicit formula comes from this idea

Step-by-step explanation:

A. An arithmetic sequence is a sequence of numbers that have a common difference. That is, for any pair of successive terms, the difference between the second and the first is the same.

If the first term is a1 and the common difference is d, then we have ...

  1st term: a1

  2nd term: a1 +d

  3rd term: a1 +d +d

  4th term : a1 +d +d +d

Perhaps you can see that the number of times d is added to the first term is 1 less than the term number. Expressed as a formula for the n-th term (an), we have ...

  an = a1 +d(n-1)

We are given that the first term is 12 and the 3rd term is 4. This is enough for us to figure out the values of a1 and d.

  1st term: a1 = 12

  3rd term: a1 +d(3-1) = 12 +2d = 4

     Subtracting 12 from both sides of this equation, we have ...

     2d = -8

     d = -4

So, the n-th term of the sequence is ...

  an = 12 -4(n -1)

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B. We know that each term of the sequence can be found by adding the common difference to the previous term. We now know the common difference is -4, so we have to agree with Daelyn that ...

  "to find the next term of the sequence, add -4 to the previous term."

Since we used this idea to derive the explicit formula, we know it is equivalent.

there is no diagram : |

step-by-step explanation:

i would say c is the best answer, hope it's right!

good luck! =)

cutie~