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Andru [333]
3 years ago
9

There are 892 students in a school. After one year they lost 194 students and by the 3rd year they lost 75 more students but got

64 more students. How many students does the school have now
Mathematics
2 answers:
djverab [1.8K]3 years ago
8 0
892 - 194 = 698

698 - 75 = 623

623 + 64 = 687 students

tensa zangetsu [6.8K]3 years ago
6 0
Solutions 

<span>There are 892 students in a school. After one year they lost 194 students. By losing 194 students the have 698 students left. B</span><span>y the 3rd year they lost 75 more students but got 64 more students. Therefore you subtract 75 from 698 and add 64 students. 

698 - 75 =  623 

623 + 64 = 687 

The school has 687 students left. </span>
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Let

S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n

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\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}

Now, we're given

a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a

a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}

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\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}

We've already confirmed r ≠ 1, so we can simplify this to

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\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12

and so the sum we want is

ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

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If you want to learn more about areas:

brainly.com/question/24487155

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