Write a formula for the general term(the nth term)of the arithmetic sequence. Do not use a recursion formula. Then use the formula for a(n) to find the indicated term of the sequence Find a(11); 12, 10, 8, ...

I came up with -10 ?

a = 12 - 2(n-1) = 14 - 2n

The n=1 term is 12 and each successive term decreases by 2.
Plug in n=11 and see what you get. I get -8.
12, 10, 8, 6, 4, 2, 0, -2, -4, -6, -8

To find the formula for the general term (the nth term) of an arithmetic sequence, we need to know two things: the first term (a) and the common difference (d).

In the given sequence, 12, 10, 8, ...

First, let's determine the first term (a) and the common difference (d).

The first term (a) is 12, as it is the first number in the sequence.

Now, let's find the common difference (d). To do this, we can subtract any two consecutive terms in the sequence. Let's subtract the second term (10) from the first term (12):

d = 10 - 12
d = -2.

So, we have the first term (a = 12) and the common difference (d = -2).

Now we can use the formula for the general term (the nth term) of an arithmetic sequence:

a(n) = a + (n - 1) * d.

In this formula, a(n) represents the nth term of the sequence, a is the first term, n is the term number, and d is the common difference.

Now let's find the 11th term, a(11), using the formula:

a(11) = a + (11 - 1) * d.

Substituting the values of a and d we found earlier:

a(11) = 12 + (11 - 1) * (-2).

Simplifying the expression:

a(11) = 12 + 10 * -2.

a(11) = 12 + (-20).

a(11) = -8.

Therefore, the 11th term (a(11)) of the given sequence, 12, 10, 8, ... is -8, not -10.