How do you find the first term in the arithmetic sequence __, 8 1/3, 7, 5 2/3, 4 1/3, ...?

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How do you find the first term in the arithmetic sequence __, 8 1/3, 7, 5 2/3, 4 1/3, ...?

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Answer 1 · 2018-07-02T10:37:26

$9 \frac{2}{3}$ $9 2/3$

Explanation:

$the common difference d of the sequence is$ $"the common difference d of the sequence is"$

$∙ x d = a_{2} - a_{1} = a_{3} - a_{2} = a_{4} - a_{3}$ $•color(white)(x)d=a_2-a_1=a_3-a_2=a_4-a_3$

$d = 7 - 8 \frac{1}{3} = 5 \frac{2}{3} - 7 = - \frac{4}{3}$ $d=7-8 1/3=5 2/3-7=-4/3$

$\Rightarrow a_{1} = a_{2} - d = 8 \frac{1}{3} - (- \frac{4}{3}) = \frac{29}{3} = 9 \frac{2}{3}$ $rArra_1=a_2-d=8 1/3-(-4/3)=29/3=9 2/3$

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How do you find the first term in the arithmetic sequence __, 8 1/3, 7, 5 2/3, 4 1/3, ...?

1 Answer

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