Question

Fill in the blanks to make an arithmetic sequence

Answer 1

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General Equation:
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$T_n = a_1 + d(n - 1)$

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Find d :
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$a_1 = 11, T_7 = 79,$
$T_7 = 11 + d(7 - 1)$
$-79 = 11 + 6d$
$6d = -79 - 11$
$6d = -90$
$d = -15$

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Find general equation :
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$T_n = 11 + (-15)(n - 1)$
$T_n = 11 -15n + 15$
$T_n = 26 -15n$

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

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