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anonymous

  • one year ago

Identify the sequence graphed below and the average rate of change from n = 1 to n = 3. coordinate plane showing the point 1, 8, point 2, 4, point 4, 1, and point 5, .5

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    \[a_1=8=2^3\] \[a_2=4=2^2\] \[a_4=1=2^0\] \[a_5=0.5=2^{-1}\] this one's not in there but you should see the pattern well enough to write the sequence \[a_3=2=2^1\]

  3. anonymous
    • one year ago
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    @peachpi those look like none of my question choices. im so confued

  4. anonymous
    • one year ago
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    the pattern between points is multiplying by ½, so that's the common ratio, r. The sequence is geometric. The formula for a geometric sequence is \[a_n=a_1 r^{n-1}\]

  5. anonymous
    • one year ago
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    r is ½. a_1 is the first term of the sequence

  6. anonymous
    • one year ago
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    Identify the sequence graphed below and the average rate of change from n = 1 to n = 3. coordinate plane showing the point 1, 8, point 2, 4, point 4, 1, and point 5, .5 A) an = 8(one half)n − 1; average rate of change is −3 B) an = 10(one half)n − 1; average rate of change is 3 C)an = 8(one half)n − 1; average rate of change is 3 D) an = 10(one half)n − 1; average rate of change is −3 Those are my answer choices @peachpi

  7. anonymous
    • one year ago
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    ok. use the formula I just put up to get a formula for a_n

  8. anonymous
    • one year ago
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    |dw:1435250004835:dw|

  9. anonymous
    • one year ago
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    okay then then what

  10. anonymous
    • one year ago
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    @peachpi what would the correct answer be

  11. Michele_Laino
    • one year ago
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    your terms represent a geometric sequence, whose first term is 8 and the constant is 1/2. Now the general term of a geometric sequence is given by the subsequent formula: \[\Large {a_n} = {a_1}{q^{n - 1}}\] please substitute q=1/2 and a_1=8, what do you get?

  12. anonymous
    • one year ago
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    4?

  13. Michele_Laino
    • one year ago
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    hint: \[\Large {a_n} = {a_1}{q^{n - 1}} = 8 \times {\left( {\frac{1}{2}} \right)^{n - 1}}\] am I right?

  14. anonymous
    • one year ago
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    yes

  15. Michele_Laino
    • one year ago
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    ok! that is your answer!

  16. anonymous
    • one year ago
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    A) an = 8(one half)n − 1; average rate of change is −3 B) an = 10(one half)n − 1; average rate of change is 3 C)an = 8(one half)n − 1; average rate of change is 3 D) an = 10(one half)n − 1; average rate of change is −3 out of these which woud it be?

  17. Michele_Laino
    • one year ago
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    for example if we set n=2, we get: \[\Large {a_2} = 8 \times {\left( {\frac{1}{2}} \right)^{2 - 1}} = 8 \times \frac{1}{2} = 4\] similarly for other terms

  18. Michele_Laino
    • one year ago
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    if we set n=3, we get: \[\Large {a_3} = 8 \times {\left( {\frac{1}{2}} \right)^{3 - 1}} = 8 \times \frac{1}{{{2^2}}} = 8 \times \frac{1}{4} = 2\]

  19. anonymous
    • one year ago
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    still confused for what the avg. rate of change would be

  20. Michele_Laino
    • one year ago
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    now the requested change rate, can be this:

  21. anonymous
    • one year ago
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    - 3 or 3??

  22. Michele_Laino
    • one year ago
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    \[\large r = \frac{{{a_1} + {a_2} + {a_3} + {a_4}}}{4} = \frac{{8 + 4 + 2 + 0.5}}{4} = ...\]

  23. anonymous
    • one year ago
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    3.625

  24. Michele_Laino
    • one year ago
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    that's right!

  25. anonymous
    • one year ago
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    so the correct answer is C?

  26. Michele_Laino
    • one year ago
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    yes I think so!

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