Total lost on this question.
Question: Write a rule for the nth term of the sequence. Use your rule to find a100.–8, 9, 26, 43, 60, . . .
How far I've gotten (don't know if I'm even doing this right): Okay so I see that the difference in the sequence is an increase of 17. So the rule would be an = - 25 + 17n . So now we can use this to find the 100th term. So now to find the 100th term we use the rule a*100 = - 25 + 17*100 =

Question

Total lost on this question.
Question: Write a rule for the nth term of the sequence. Use your rule to find a100.–8, 9, 26, 43, 60, . . .
How far I've gotten (don't know if I'm even doing this right): Okay so I see that the difference in the sequence is an increase of 17. So the rule would be an = - 25 + 17n . So now we can use this to find the 100th term. So now to find the 100th term we use the rule a*100 = - 25 + 17*100 =

whpalmer4 · Answer

$$a_0 = -8$$$$ a_1 = 9$$Right? Does your rule work?
$$a_n = -25 + 17n$$$$a_1 = -25 + 17(1) = 8$$
Looks like you have an "off by one" error in there, unless the first term of the sequence is really -25, not -8 as the problem seems to state.  You are on the right track!

whpalmer4 · Answer

Try solving the equation for a0.  You've got the right difference, but the wrong starting condition.

anonymous · Answer

Not really sure, do you mean a0 = - 25 + 17(1) = 8? Then solve for a0?

whpalmer4 · Answer

No, isn't a0 = -8?

whpalmer4 · Answer

and if you are looking to find a0, n = 0

whpalmer4 · Answer

$$a_0 = -25 + 17(0) = -8?$$  What do you have to do to make that formula work, if you can't change a0 or 0?

anonymous · Answer

Um a0 = - 25 + 17(0) = - 8 = a0 = - 25 = - 8?

whpalmer4 · Answer

Are we agreed that a1 = 9, a2 = 26, a3 = 43, a4 = 60?

whpalmer4 · Answer

and that $$a_{n+1} = a_n + 17$$

anonymous · Answer

Yeah.

whpalmer4 · Answer

So $$a_{0+1} = a_0 + 17$$but $$a_1 = 9$$ so $$a_1 = 9 = a_0 + 17$$$$a_0 = -8$$

$$a_1 = a_0 + 17$$
$$a_2 = a_1 + 17 = (a_0 + 17)+ 17$$
$$a_3 = a_2 + 17 = (a_1 + 17) + 17 = ((a_0 + 17) + 17) + 17$$
$$a_n = a_0 + 17n$$

anonymous · Answer

Okay, but how do you use the rule to find the hundreth term?

whpalmer4 · Answer

n = 100
$$a_n = a_0 + 17(100)$$

whpalmer4 · Answer

You know what, you should look at your text and see if they like to start the sequence with n = 0 or n = 1.  I did it with n = 0, but if the convention in your book is n = 1, you had the right formula already!  

n = 100
$$a_{100} = -25 + 17(100) = $$

Sorry for the confusion!

anonymous · Answer

Okay so a100 = - 25 + 17*100 = a100 = - 25 + 1700?

whpalmer4 · Answer

Yes, I believe so.

anonymous · Answer

Is there any other steps? Do we subtract 25 from 1700?

whpalmer4 · Answer

That would make it look neater, yes, but the value is the same...

anonymous · Answer

Okay, thanks for the help, it makes sense now.

whpalmer4 · Answer

Glad to hear I did no lasting harm!