1. Use the given arithmetic sequence to answer the following problems.

Arithmetic sequence: 10, 15, 20, 25, 30, ….

a. Use the formula to find the 75th Term of the given Arithmetic Sequence
I. Formula:
II. Work:

b. Use the formula to find the nth Term of the given Arithmetic Sequence

I. Formula:
II. Work:

c. Explain in words how arithmetic sequences can be written as a linear equation then write the linear equation for the arithmetic equation you found in problem b.-II.

What is your problem? There is nothing to answer to.

You can not copy and paste to this board

Is that what you want to do well probably something is wrong cause in my computer it does work. Try to see what is wrong you are probably cutting and then pasting instead of copy paste!! :)

It is a function of this particular web site Samy. Students can not paste to the board.

a. To find the 75th term of the arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence. The formula is:

nth term = first term + (n - 1) * common difference

In this formula, the first term is 10, the common difference is 5 (as each term increases by 5), and we want to find the 75th term. Plugging these values into the formula, we get:

75th term = 10 + (75 - 1) * 5
= 10 + 74 * 5
= 10 + 370
= 380

Therefore, the 75th term of the arithmetic sequence is 380.

b. To find the nth term of any arithmetic sequence, we can use the same formula as before. The formula is:

nth term = first term + (n - 1) * common difference

Where the first term is 10, the common difference is 5, and we want to find the nth term. Plugging these values into the formula, we get:

nth term = 10 + (n - 1) * 5

Therefore, the formula for the nth term of the given arithmetic sequence is 10 + (n - 1) * 5.

c. Arithmetic sequences can be written as a linear equation because they exhibit a constant difference between consecutive terms. In other words, the linear equation represents a relationship between the term number (n) and the corresponding term in the sequence.

For the arithmetic sequence we found in problem b-II, the linear equation would be:

y = 10 + (n - 1) * 5

In this equation, y represents the nth term of the sequence and n represents the term number. The expression (n - 1) * 5 represents the common difference, and adding it to the first term (10) gives us the corresponding term in the sequence.