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2 years ago

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Homework Progress 0 Find the nth term of the following sequence: 4 7 12 19 28

1 answer:

just olya [345]2 years ago

5 0

<em>Answer:</em>

n²+3

<em>Explanation:</em>

The differences between the terms are not the same, so this is not "linear". Knowing that the sequence may have started with a 1, you can try subtracting the first number with a number to get 1, and use that number to subtract the rest.

4 - 3 = 1
7 - 3 = 4
12 - 3 = 9
19 - 3 = 16
28 - 3 = 25

In this case, subtracting 3 to all the numbers gave us perfect squares! So this means the nth term has to do with squaring the number and adding three afterward! This can be checked.

√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5

As we found the values of these terms by subtracting three first and then finding its square root, the nth term will be the opposite; squaring and then adding three! Again, this can be checked!

1² + 3 = 4
2² + 3 = 7
3² + 3 = 12
4² + 3 = 19
5² + 3 = 28

Hope this helps !! :D

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3 years ago

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4 years ago

An inlet pipe on a swimming pool can be used to fill the pool in 33 hours. The drain pipe can be used to empty the pool in 34 ho

Talja [164]

<u>Answer: </u>

An inlet pipe on a swimming pool can be used to fill the pool in 33 hours. Time it will take to fill the pool = 748 hrs

<u>Solution: </u>

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$\frac{1}{33}$ = work rate of inlet pipe

$\frac{1}{34}$ = work rate of drain pipe

Using the formulae

Volume of flow=work rate $\times$ time

Let us assume complete time of pool to fill = 1

Remaining fraction of pool to be filled = $1-\frac{1}{3}=\frac{2}{3}$

$\begin{array}{l}{\frac{1}{33} x-\frac{1}{34} x=\frac{2}{3}} \\\\ {\frac{x}{33}-\frac{x}{34}=\frac{2}{3}}\end{array}$

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$\begin{array}{l}{x=\frac{2244}{3}} \\\\ {x=\frac{3168}{3}} \\\\ {x=748}\end{array}$

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3 years ago

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