How do you complete the statement for the arithmetic sequence: -14 is the __ term of 2 1/5, 2, 1 4/5,...?

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How do you complete the statement for the arithmetic sequence: -14 is the __ term of 2 1/5, 2, 1 4/5,...?

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Answer 1 · 2017-02-20T21:53:40

82nd

Explanation:

We know that the nth term of an arithmetic sequence is given by $t_{n} = a + (n - 1) d$ $t_n = a + (n - 1)d$ . Our first term is $2 \frac{1}{5} = \frac{11}{5}$ $2 1/5 = 11/5$ and our common difference is $- \frac{1}{5}$ $-1/5$ .

$- 14 = \frac{11}{5} + (n - 1) - \frac{1}{5}$ $-14 = 11/5 + (n - 1)-1/5$

$- 14 = \frac{11}{5} - \frac{1}{5} n + \frac{1}{5}$ $-14 = 11/5 - 1/5n + 1/5$

$- 14 = \frac{12}{5} - \frac{1}{5} n$ $-14 = 12/5 - 1/5n$

$- 14 - \frac{12}{5} = - \frac{1}{5} n$ $-14 - 12/5 = -1/5n$

$- \frac{82}{5} = - \frac{1}{5} n$ $-82/5 = -1/5n$

$n = \frac{- \frac{82}{5}}{- \frac{1}{5}}$ $n = (-82/5)/(-1/5)$

$n = 82$ $n = 82$

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How do you complete the statement for the arithmetic sequence: -14 is the __ term of 2 1/5, 2, 1 4/5,...?

1 Answer

Explanation:

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