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Rachel98

  • 3 years ago

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 =

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  1. whpalmer4
    • 3 years ago
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    \[a_0 = -8\]\[ a_1 = 9\]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!

  2. whpalmer4
    • 3 years ago
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    Try solving the equation for a0. You've got the right difference, but the wrong starting condition.

  3. Rachel98
    • 3 years ago
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    Not really sure, do you mean a0 = - 25 + 17(1) = 8? Then solve for a0?

  4. whpalmer4
    • 3 years ago
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    No, isn't a0 = -8?

  5. whpalmer4
    • 3 years ago
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    and if you are looking to find a0, n = 0

  6. whpalmer4
    • 3 years ago
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    \[a_0 = -25 + 17(0) = -8?\] What do you have to do to make that formula work, if you can't change a0 or 0?

  7. Rachel98
    • 3 years ago
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    Um a0 = - 25 + 17(0) = - 8 = a0 = - 25 = - 8?

  8. whpalmer4
    • 3 years ago
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    Are we agreed that a1 = 9, a2 = 26, a3 = 43, a4 = 60?

  9. whpalmer4
    • 3 years ago
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    and that \[a_{n+1} = a_n + 17\]

  10. Rachel98
    • 3 years ago
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    Yeah.

  11. whpalmer4
    • 3 years ago
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    So \[a_{0+1} = a_0 + 17\]but \[a_1 = 9\] so \[a_1 = 9 = a_0 + 17\]\[a_0 = -8\] \[a_1 = a_0 + 17\] \[a_2 = a_1 + 17 = (a_0 + 17)+ 17\] \[a_3 = a_2 + 17 = (a_1 + 17) + 17 = ((a_0 + 17) + 17) + 17\] \[a_n = a_0 + 17n\]

  12. Rachel98
    • 3 years ago
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    Okay, but how do you use the rule to find the hundreth term?

  13. whpalmer4
    • 3 years ago
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    n = 100 \[a_n = a_0 + 17(100)\]

  14. whpalmer4
    • 3 years ago
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    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!

  15. Rachel98
    • 3 years ago
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    Okay so a100 = - 25 + 17*100 = a100 = - 25 + 1700?

  16. whpalmer4
    • 3 years ago
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    Yes, I believe so.

  17. Rachel98
    • 3 years ago
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    Is there any other steps? Do we subtract 25 from 1700?

  18. whpalmer4
    • 3 years ago
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    That would make it look neater, yes, but the value is the same...

  19. Rachel98
    • 3 years ago
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    Okay, thanks for the help, it makes sense now.

  20. whpalmer4
    • 3 years ago
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    Glad to hear I did no lasting harm!

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