Question

The sum of 6 consecutive even numbers is 270.What is the second number in this sequence?

Answer 1

Answer: 42

Step-by-step explanation:

Let the six consecutive even numbers be x , x+2 , x+4 ,x+6 ,x+8 ,x+10.

Then According to the question , we have

$x+(x+2)+(x+4)+(x+6)+(x+8)+(x+10)=270\\\\\Rightarrow\ x+x+2+x+4+x+6+x+8+x+10=270\\\\\Rightarrow\6x+30=270\\\\\Rightarrow\ 6x=270-30\\\\\Rightarrow\ 6x=240\\\\\Rightarrow\ x=40$

Now, the second number from the above six consecutive even numbers  is x+2.

Substitute the value of x in it, we get

The second number in this sequence = $x+2=40+2=42$

Answer 2

Even numbers are those that end in 0, 2, 4, 6, and 8. The second number in this sequence is 42.

What is an even number?

A number that is divisible by two into two equal whole numbers is called an even number. Even numbers are those that end in 0, 2, 4, 6, and 8.

Let the first even number be represented by 2n. Therefore, the other five consecutive even numbers will be,

• Second number = (2n+2)
• Third number = (2n+4)
• Fourth number = (2n+6)
• Fifth number = (2n+8)
• Sixth number = (2n+10)

As it is given that the sum of the six numbers is 270. Therefore, the sum can be written as,

$2n+(2n+2)+(2n+4)+(2n+6)+(2n+8)+(2n+10)=270\\\\2n+2n+2+2n+4+2n+6+2n+8+2n+10=270\\\\6(2n)+30=270\\\\12n=240\\\\n = 20$

Further, the second number in this sequence is represented by (2n+2), therefore, if we substitute the value of n we will get,

$2n+2\\\\=2(20)+2\\\\=40+2\\\\=42$

Thus, the second number in this sequence is 42.

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