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3 years ago

Four dates in a row have a sum of 74.what are the dates?

Mathematics

1 answer:

Hunter-Best [27]3 years ago

6 0

X+x+1+x+2+x+3=74
4x+6=74
4x=74-6
4x=68
x=68/4
x=17
17
17+1=18
17+2=19
17+3=20

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Klio2033 [76]

First part of question:

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The general term for geometric series is:

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$a_{1}$ = the first term of the series

$r$ = the geometric ratio

$a_{1}$ would represent the height at which the ball is first dropped. Therefore:

$a_{1} = k$

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Our general term would be:

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$a_{n}=k(\frac{3}{4}) ^{n-1}$

Second part of question:

If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.

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$n$ represents the number of times the ball bounces:

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Plugging this back into our general term of the geometric series:

$a_{n}=k(\frac{3}{4}) ^{n-1}$

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$S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$

We already know these variables:

$a_{1}= k = 235\ ft$

$r=\frac{3}{4}$

$n = 12$

Therefore:

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{1-\frac{3}{4} }$

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{\frac{1}{4} }$

$S_{n}=(4)(235)(1-\frac{3}{4} ^{12})$

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