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Veronika [31]
3 years ago
14

The sum of 5 consecutive even numbers is 200. what is the fifth number in this sequence

Mathematics
2 answers:
Andrej [43]3 years ago
8 0
Answer: 44

solution: x+(x+2)+(x+4)+(x+6)+(x+8)=200
5x+20=200
5x=180
x=36
5th number - x+8=36+8=44
Deffense [45]3 years ago
7 0

Answer:

The fifth number in this sequence is 44.        

Step-by-step explanation:

Given : The sum of 5 consecutive even numbers is 200.

To find : What is the fifth number in this sequence?

Solution :

Let the 5 consecutive even numbers are x,(x+2),(x+4),(x+6),(x+8)

The sum of 5 consecutive even numbers is 200.

i.e. x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 200

Solving the equation,

5x+20= 200

5x=180

x=\frac{180}{5}

x=36

So, The numbers are

First number x=36

Second number x+2=36+2=38

Third number x+4=36+4=40

Fourth number x+6=36+6=42

Fifth number x+8=36+8=44

Therefore, The fifth number in this sequence is 44.

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7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54} simplified as 11\sqrt{3}- 7\sqrt{6} or 1.909 .

<u>Step-by-step explanation:</u>

We need to Simplify seven square root of three end root minus four square root of six end root plus square root of forty eight end root minus square root of fifty four. Which is equivalent to 7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54} :

7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}

⇒ 7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{44}

⇒ 7\sqrt{3}- 4\sqrt{6} + \sqrt{16(3)} - \sqrt{9(6)}

⇒ 7\sqrt{3}- 4\sqrt{6} + 4\sqrt{(3)} - 3\sqrt{(6)}

⇒ 11\sqrt{3}- 4\sqrt{6}- 3\sqrt{(6)}

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⇒ 11(1.723)- 7(2.449)

⇒ 1.909

Therefore, 7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54} simplified as 11\sqrt{3}- 7\sqrt{6} or 1.909 .

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