In an arithmetic sequence, the first term is 100 and the sixth term is 85. Find the common difference. Then, find the 50th term of the sequence.

Do I use the formula an=a1+(n-1)d?
If so, what would my "n" by in the equation?

The nth term of an arithmetic progression is defined by N = a + (n-1)d where N = the nth term, a = the first term and d = the common difference.

Therefore,
85 = 100 + (6 - 1)d
-15 = 5d making d = -3

The 50th term then becomes
N(50) = 85 + (50 - 1)(-3) = ?

ah what!!!!!!!!!!!!!!!!!!!

Yes, you can use the formula an = a1 + (n-1)d to find the nth term in an arithmetic sequence, where a1 is the first term, d is the common difference, and n is the term number you want to find.

In this case, you are given the first term (a1 = 100) and the sixth term (a6 = 85). You want to find the common difference (d) and the 50th term (a50).

To find the common difference (d), you can use the formula:

a6 = a1 + (6-1)d

Plugging in the given values:

85 = 100 + 5d

Now, you can solve for d:

85 - 100 = 5d

-15 = 5d

d = -15/5

d = -3

So, the common difference is -3.

To find the 50th term (a50), you can use the same formula, but this time the term number is 50:

a50 = a1 + (50-1)d

Substituting the values:

a50 = 100 + (50-1)(-3)

Simplifying the expression:

a50 = 100 + 49(-3)

a50 = 100 - 147

a50 = -47

Therefore, the 50th term of the sequence is -47.

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