Question

What is the 43rd term of an arithmetic sequence with a rate of increase of -6 and a11 = 12?

Answer 1

Do you have answer choices? I got that a_43 = -180

Answer 2

Just in case you're wondering...I used the formula\[a _{n}=a _{1}+(n-1)d\] We have the fact that a_11 = 43, we also know d = -6. So in order to find the 43rd term, you have to find a_1, which is the first term. Using the info we have we can solve for a_1 like this:

Answer 3

If \[a _{11}=12\]then\[12=a _{1}+[(11-1)( -6)]\]

Answer 4

That simplifies to \[12=a _{1}+(10 * -6)\]which simplifies further to give you\[12=a _{1}-60\]and solving for a_1, we get\[a _{1}=72\]

Answer 5

Now that we know the first term, we go back to our original formula and use it to find the 43rd term like this:

Answer 6

\[a _{43}=72+(43-1)(-6)\]\[a _{43}72+(42 * -6)\]\[a _{43}=72-252\]\[a _{43}= -180\]Hope you're around to see this!