Question

The formula for any arithmetic sequence is an = a1 + d(n - 1), where a represents the value of the nth term, a1 represents the value of the first term, d represents the common difference, and n represents the term number. What is the formula for the sequence -15, -11, -7, ...?

an = -15 + (-4)( n - 1)
an = -15 + ( n - 1)
an = 4 + (-15)( n - 1)
an = -15 + 4( n - 1)

Answer 1

an=-15+4(n-1)

Explanation:

The formula for the sequence -15, -11, -7... is

an=-15+4(n-1)

because -15 is the first term in the sequence and when you add 4 to -15 you get -11. you add 4 to -11 and you get -7. 4 is your common difference so that would go outside of your parenthesis and n-1 goes inside the parenthesis so then the answer is an=-15+4 (n-1)

(Hope you understood this...if you want to check it yourself you can get a calculator and add 4 to -15 and you should get -11 and when you add 4 you should get -7. If wrong then I'm sorry)

Answer 2

The formula for any arithmetic sequence is an = a1 + d(n - 1), where a represents the value of the nth term, a1 represents the value of the first term, d represents the common difference, and n represents the term number.

In the sequence -15, -11, -7, ..., the first term is -15, and the common difference is -4. Therefore, the formula for this sequence is an = (-15) + (-4)( n - 1).

This simplifies to an = -15 + (-4)( n - 1), which is the correct answer.

The other formulas listed in the question do not accurately represent the sequence -15, -11, -7, ..., because they do not include the correct values for the first term and common difference of the sequence. For example, the formula an = 4 + (-15)( n - 1) includes the correct common difference, but the first term is incorrect. Similarly, the formula an = -15 + 4( n - 1) includes the correct first term, but the common difference is incorrect. Therefore, these formulas do not accurately represent the sequence -15, -11, -7, ..., and the correct answer is an = -15 + (-4)( n - 1).