Question

Find an equation for the nth term of the arithmetic sequence.a16 = 21, a17 = -1
OPTIONS:

an = 351 + 22(n + 1)

an = 351 - 22(n + 1)

an = 351 + 22(n - 1)

an = 351 - 22(n - 1)

I GIVE MEDALS ! PLEASE HELP

Answer 1

Plug in the values you have and see which one works. For example:
\[a_n = 351 + 22(n+1)\]\[a_{16} = 351+22(16+1) = 351+374\]Clearly not that one! Be careful, you want to make sure that both numbers work...

Answer 2

@whpalmer4 how do you know if it works or not ?

Answer 3

As I said, plug in the values and see if you get the right answer. With that first formula, plugging in n = 16 did not give us 21, but a16 = 21, so that's not the correct formula.

Answer 4

no now ill do a17=351+22(17+1) right ?

Answer 5

Well, let's make life easier and engage brain before pencil :-) Look at the structure of those equations. Some of them are 351 + 22*something, and some are 351 - 22*something. The something is always positive, so the ones where we add we're going to have a result that is > 351, right? Our desired values are 21 and -1.

Answer 6

To me, that says we don't have to bother trying out anything that is of the form 351 + 22(something) because there's just no chance of it being the right answer.

Answer 7

The answer is D then !

Answer 8

Let's check:
\[a_{16} = 351 - 22(16-1) = 351 - 330 = 21\checkmark\]
\[a_{17} = 351-22(17-1) = 351 - 352 = -1\checkmark\]
Looks good!

Answer 9

YES! thank you ... what about another ?

Answer 10

I guess I have time for one more...

Answer 11

A certain species of tree grows an average of 3.1 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 600 centimeters tall.

Ive been stuck on how to even do this It looks easy but ehh nothing

Answer 12

im thinking H(n)=600+3.1*n

Answer 13

there the H(n) to represent the number of weeks is n

Answer 14

if n is the number of weeks, that looks good to me. at n = 0, H(n) = 600+3.1(0) = 600, which is the initial condition we were given. After 1 week, n = 1, H(1) = 600+3.1(1) = 603.1, which is what we would expect, too.

Answer 15

So I am right ?

Answer 16

Yes, I just checked your work, didn't you agree? :-)

Answer 17

yes Thank you !