Question

Fill in the blanks to make an arithmetic sequence

11, _ , _ , _ , _ , _ , -79

Show all work :)

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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