Question

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

Answer 1

@iGreen

Answer 2

@Night-Watcher

Answer 3

@John_ES

Answer 4

An arithmetic sequence has a general form like this,
\[a_n=a_1+d\cdot(n-1)\]with d, the distance between two consecutive terms. You can deduce from the problem that, d=-6, and that a_11=12 when n is equal to 11. Can you follow from this point?

Answer 5

The answer choices are:
a: -174
b: -176
c: -180
d: -186
e: -240
The answer I got wasnt on the list. so i probably am really confused with this

Answer 6

The first thing you need is a_1. In order to obtain it let's introduce the data of the problem
\[a_{11}=12=a_1+(-6)(11-1)\Rightarrow a_1=72\] Do you understand this step?

Answer 7

Yes.

Answer 8

Now, you can calculate a_43, the only thing you need to do is put n=43 in the general form,
\[a_{43}=72+(-6)(43-1)=\] Do it.

Answer 9

-180

Answer 10

Exactly.

Answer 11

Ohhh. I got it. Thanks so much!!

Answer 12

You're welcome.