# The sum of four consecutive odd integers?

The sum of four consecutive odd integers is three more than 5 times the least of the integers.

Update:

I don't get the last part, I get the four consecutive integers, though.

Relevance
• Anonymous

Any odd integer can be written as (2n + 1) for some integer n. The 2n is even and adding the one makes it odd.

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So the four integers are:

2n + 1

2n + 3

2n + 5

2n + 7..............................and their total is:

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8n + 16

So 8n+ 16 = 3 + 5*(2n + 1)......Expand the right hand side of this equation.

8n + 16 = 3 + 10n + 5......Subtract 8n from both sides.

16 = 2n + 8...........Subtract 8 from both sides

8 = 2n..................Divide both sides by 2

4 = n

n = 4

The integers are ((2*4) + 1) = 9 and then 11, 13, and 15.

Now to check the answer: 9+11+13+15 = 48

48 ?= 3 + (5*9)

48 ?= 3 + 45

48 ?= 48......Yes it does. So the answers check and are valid.

Summarizing. The integers are 9, 11, 13, and 15...<<..Answer

• Let x be the smallest integer. Since they are consecutive odd, there is a difference of two between each one, so the three other integers are x + 2, x + 4, and x + 6. The sum of all of those is three more than 5 times the least. Remember that the least integer is x, so you have 5 times that, which would be 5x, and then 3 more added on to it, which is 5x + 3:

x + (x + 2) + (x + 4) + (x + 6) = 5x + 3

4x + 12 = 5x + 3

12 = x + 3

9 = x

ANSWER: The integers are 9, 11, 13, and 15.

• Least of the integers (x):

5x + 3 = x + x + 2 + x + 4 + x + 6

x = 9

2nd integer:

= 9 + 2

= 11

3rd integer:

= 9 + 4

= 13

4th integer:

= 9 + 3

= 15

Answer: 9, 11, 13 & 15 are the integers.

Proof (3 is the difference after deducting 5 times the least of integers from the sum of all integers):

= (9 + 11 + 13 + 15) - 5(9)

= 48 - 45

= 3

• x is the lowest integer, since the integers are odd, they go up by 2 from the lowest number

x + (x+2) + (x + 4) + (x + 6) = 5x + 3

Simplify by adding the xs and numbers

4x + 12= 5x + 3

Subtract 4x from both sides

12 = x + 3

Subtract 3 from both sides

9 = x

9 is the lowest integer, and just add two to that each time to get the consecutive odd integers

the integers are 9, 11, 13, and 15

• Anonymous

x + (x+2) + (x+4) + (x+6) = 5x +3

4x +12 = 5x + 3

9 = x

so the numbers are: 9, 11, 13, 15 = 48

5(9) + 3 = 48 checks

• 2n+1 is an odd interger #1

2n+1+2n+3+2n+5+2n+7=3+5(2n+1)

8n+16=3+10n+5

8n+16=10n+8

8=2n

4=n

the numbers are

2(4)+1=9

2(4)+3=11

2(4)+5=13

2(4)+7=15

• enable x be the 1st type. x+x+2+x+4+x+6=216. 4x+12=216. 4x=204 x=fifty one Numbers are atypical and sequential (or use the algebra i.e x, x+2, x+4 etc), so series is fifty one, fifty 3, fifty 5, fifty seven.