Question

A(n) = 12 + (n - 1)(-4)

Answer 1

Find the third, sixth, and twentieth terms of the sequence described by the following rule. Be sure to show all of your work.

Answer 2

start with
A(n) = 12 + (n - 1)(-4)

for the third term, replace n with 3
can you write down what you get ?

Answer 3

Everywhere you see "n", erase it, and put in 3 instead

Answer 4

Got it ;) Thank you so much! @phi

Answer 5

Wait then what do I do with A?? @phi

Answer 6

And what do I do for the sixth and twentieth terms? Do I replace the sixth with 6 and twentieth with 20?

Answer 7

A(n) is just a "name" for a term
A(3) is the third term
you do not need it.

Answer 8

Do I replace the sixth with 6 and twentieth with 20?

Exactly. the formula tells you how to find any term you want.

Answer 9

And so the sixth term would be A(6) and the twentieth would be A(20) correct??

Answer 10

yes, but those are the names. they want the actual number, so for example
A(6) = 12+(6-1)(-4)
now simplify the right side

Answer 11

The right side would be -8... So do I multiply that by 6? Or is -8 the answer?

Answer 12

yes, A(6) = -8
that says " the sixth term is -8"
-8 is the answer. But I would write A(6)=-8 to make it clear.

Answer 13

Okay I got it! Thank you very much for your help!

Answer 14

btw, A(n) does not mean A times n . It is just a way to say the nth term of A
you have to get used to this way of writing things. Algebra mostly sticks to rules, but there are these strange conventions you have to memorize.

Answer 15

Okay! Got it! Thank you for your time! :))

Answer 16

sometimes you see it this way
\[ A_n\]
which means the same thing, the nth term of A

Answer 17

So no multiplication between the two... Got it. Thanks.