Question

Question #fcc37

Answer 1

`53`

Explanation:

let`" "n" "`be the middle number

then we have
1st number`=n-2`

2nd number`=n-1`

4th number `n+1`

5th number`=n+2`

`(n-2)+(n-1)+n+(n+1)+(n+2)=270`

`n-cancel(2)+n-cancel(1)+n+n+cancel(1)+n+cancel(2)=270`

`5n=270`

`n=270/5=54`

`2nd" number "=54-1=53`

Answer 2

Entire sequence: `52, 53, 54, 55, 56`
Second number in the sequence: `53`

Explanation:

If the sum of consecutive integers is equal to `270`, we can write the first integer as `x`, the 2nd as `x+1` (because they are consecutive), etc.

• First integer: `x`
• Second integer: `x+1`
• Third integer: `x+2`
• Fourth integer: `x+3`
• Fifth integer: `x+4`

Notice with each integer, you are increasing the number by `1`. If that seems confusing, think about it this way:

If the first integer was `x`, the second will be `x+1`. With the third integer, we still increase by one from the previous integer:

`(x+1) ul(+1) = x+2`

Let's set up our equation:

`x+(x+1)+(x+2)+(x+3)+(x+4)= 270`

We have a good deal of terms to combine, so let's do that.

`x+x+x+x+x=5x`

`1+2+3+4= 10`

From this, we can make our new equation

`5x+10=270`

Subtract `10` from both sides to get

`5x=260`

Divide both sides by `5` to get

`x=52`

This isn't our answer, however. We found what `x` is (the first integer), but we want to know the second number in this sequence is, and to do that, just plug `52` into our expression for the second integer, `(x+1)`

`52+1= 53`

The second integer is `53`.