ParthKohli
  • ParthKohli
I found this easy problem in the grade 8th entrance exam... try it :-) Let \(\large x_1, x_2, x_3 \cdots x_n\) be a sequence such that \(\large \sum \limits_{i = 1}^{n} (x_i - 3) = 170 \) and \(\large \sum \limits_{i = 1}^{n} (x_i - 6) = 50\). What is the value of \(n\)?
Mathematics
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SOLVED
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katieb
  • katieb
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goformit100
  • goformit100
0k ?
anonymous
  • anonymous
Okay, it's not a hard problem, but it is tedious and requires knowledge about summations that is barely touched in many algebra 2 classes.
anonymous
  • anonymous
Multiply the first equation by \(-2\) and then add it to the second equation.

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BAdhi
  • BAdhi
$$\sum \limits_{i=1}^nx_i=p\\ \sum\limits_{i=1}^nx_i-\sum\limits_{i=1}^n3=170 \implies p-3n=170\qquad (1)\\ \sum\limits_{i=1}^nx_i-\sum\limits_{i=1}^n6=50\implies p-6n=50 \qquad(2)$$ (1)-(2) 3n=120 => n=40
ParthKohli
  • ParthKohli
@BAdhi :-D

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