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katherinekc

  • 2 years ago

Find an equation for the nth term of the arithmetic sequence. a10 = 32, a12 = 106

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  1. genius12
    • 2 years ago
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    Firstly, the formula of for a term of an arithmetic sequence is given by:\[x _{n}=a+(n-1)d\]Where a is the first term, n is the term number, d is the common difference. Since we know this is an arithmetic sequence, then a11 is the average of a10 and 12. Therefore: a11 = (32 + 106) / 2 = 138 / 2 = 69 Now we have the sequence: 32, 69, 106. Since this is an arithmetic sequence, a11 - a10 gives us the common difference. d = 69 - 32 = 37. Now we got d, so we just need to find a. We can use the already given a11 to find a.\[69=a+(11-1)37 \rightarrow 60=a+370 \rightarrow a=-310\]Now we know a = -310 and = 37. We plug in these values to get the equation:\[x _{n}=-310+(n-1)37\]

  2. katherinekc
    • 2 years ago
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    oh i get it! thank you!

  3. katherinekc
    • 2 years ago
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    could you help me on this to? if you can 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 400 centimeters tall.

  4. wio
    • 2 years ago
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    A certain species of tree grows an average of 3.1 cm per week. \[ d = 3.1\]the measurements begin when the tree is 400 centimeters tall. \[a_1 = 400 \]So this means \[ a_n = a_1 +(n-1)d = 400+(n-1)3.1 \]

  5. katherinekc
    • 2 years ago
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    Ohh okay! i just couldnt figure out how to start it!! thank you!!

  6. katherinekc
    • 2 years ago
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    also, for this problem; Find an equation for the nth term of the arithmetic sequence. -3, -5, -7, -9, ... would the answer be an = -3 + -2(n - 1)?

  7. wio
    • 2 years ago
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    Yes.

  8. katherinekc
    • 2 years ago
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    okay! thank you

  9. katherinekc
    • 2 years ago
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    im sorry to be a bother.. but would this one be correct to? Find an equation for the nth term of the arithmetic sequence. 8, 6, 4, 2, ... an = 8 + -2(n - 1)?

  10. wio
    • 2 years ago
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    Yeah

  11. katherinekc
    • 2 years ago
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    okay! thank-you!

  12. 3p0huggedout
    • 7 months ago
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    a1=-1,d=-3,n=10 9th term?

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