The sum of 4 consecutive even numbers is 36. What is the first number in this sequence?

Mathematics

2 answers:

Anna [14]3 years ago

8 0

Answer:

first number = 6

Step-by-step explanation:

Note that consecutive even numbers have a difference of 2 between them.

Let n be the first even number then

n + 2, n + 4, n + 6 are the next 3 consecutive even numbers

Sum them together and equate to 36

n + n + 2 + n + 4 + n + 6 = 36 ← simplify left side

4n + 12 = 36 ( subtract 12 from both sides )

4n = 24 ( divide both sides by 4 )

n = 6

The first number is 6 and the next 3 are 8, 10, 12

sashaice [31]3 years ago

7 0

Answer:

the first number in this sequence is 6....

Step-by-step explanation:

First number = x

2nd number = x+2

3rd consecutive even number = x+4

4th consecutive even number = x+6

Therefore,

By adding these numbers:

x+x+2+x+4+x+6= 36

Add the like terms:

4x+12=36

Combine the constants:

4x=36-12

4x=24

Divide both the terms by 4

4x/4 = 24/4

x= 6

Thus the first number in this sequence is 6....

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