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saveliy_v [14]
3 years ago
12

Plzx solve it with steps....

Mathematics
1 answer:
VMariaS [17]3 years ago
6 0

I think the second number is supposed to be negative, -11/2 = -5.5, because otherwise the sequence is not arithmetic.

The <em>n</em>-th term of the sequence, starting with <em>n</em> = 1, is then

-6 + 0.5 (<em>n</em> - 1) = 0.5<em>n</em> - 6.5

and we want to find the number <em>N</em> such that

\displaystyle\sum_{n=1}^N(0.5n-6.5)=-25

We have

\displaystyle\sum_{n=1}^N(0.5n-6.5) = 0.5\sum_{n=1}^Nn-6.5\sum_{n=1}^N1\\ = 0.5\times\frac{N(N+1)}2 - 6.5N \\= 0.25N^2-6.25N = -25

Solve for <em>N</em> :

0.25 <em>N</em> ² - 6.25<em>N</em> + 25 = 0

<em>N</em> ² - 25<em>N</em> + 100 = 0

(<em>N</em> - 20) (<em>N</em> - 5) = 0

<em>N</em> = 20   <u>or</u>   <em>N</em> = 5

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Source:
http://www.1728.org/kepler3a.htm



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3 years ago
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