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Rachel98
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 =
\[a_0 = -8\]\[ a_1 = 9\]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!
Try solving the equation for a0. You've got the right difference, but the wrong starting condition.
Not really sure, do you mean a0 = - 25 + 17(1) = 8? Then solve for a0?
and if you are looking to find a0, n = 0
\[a_0 = -25 + 17(0) = -8?\] What do you have to do to make that formula work, if you can't change a0 or 0?
Um a0 = - 25 + 17(0) = - 8 = a0 = - 25 = - 8?
Are we agreed that a1 = 9, a2 = 26, a3 = 43, a4 = 60?
and that \[a_{n+1} = a_n + 17\]
So \[a_{0+1} = a_0 + 17\]but \[a_1 = 9\] so \[a_1 = 9 = a_0 + 17\]\[a_0 = -8\] \[a_1 = a_0 + 17\] \[a_2 = a_1 + 17 = (a_0 + 17)+ 17\] \[a_3 = a_2 + 17 = (a_1 + 17) + 17 = ((a_0 + 17) + 17) + 17\] \[a_n = a_0 + 17n\]
Okay, but how do you use the rule to find the hundreth term?
n = 100 \[a_n = a_0 + 17(100)\]
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!
Okay so a100 = - 25 + 17*100 = a100 = - 25 + 1700?
Is there any other steps? Do we subtract 25 from 1700?
That would make it look neater, yes, but the value is the same...
Okay, thanks for the help, it makes sense now.
Glad to hear I did no lasting harm!