4 months ago
Q:

Fill in the blanks to make an arithmetic sequence 11, _ , _ , _ , _ , _ , -79Show all work :)

Accepted Solution

A:
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General Equation:
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[tex]T_n = a_1 + d(n - 1)[/tex]

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Find d :
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[tex]a_1 = 11, T_7 = 79,[/tex]
[tex]T_7 = 11 + d(7 - 1)[/tex]
[tex]-79 = 11 + 6d[/tex]
[tex]6d = -79 - 11[/tex]
[tex]6d = -90[/tex]
[tex]d = -15[/tex]

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Find general equation :
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[tex]T_n = 11 + (-15)(n - 1)[/tex]
[tex]T_n = 11 -15n + 15[/tex]
[tex]T_n = 26 -15n [/tex]

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Find the sequence :
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[tex]T_1 = 26 - 15(1) = 11[/tex]
[tex]T_2 = 26 - 15(2) = -4[/tex]
[tex]T_3 = 26 - 15(3) = -19[/tex]
[tex]T_4 = 26 - 15(4) = -34[/tex]
[tex]T_5 = 26 - 15(5) = -49[/tex]
[tex]T_6 = 26 - 15(6) = -64[/tex]
[tex]T_7 = 26 - 15(7) = -79[/tex]

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Answer: 11, -4, -19, -34, -49, -64, -79
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