Question

Question #325c0

Answer 1

the fourth number in this sequence is `23`

Explanation:

Let's start by writing down what we know in an equation:

`x + (x+1)+(x+2)+(x+3)+(x+4)=110`

`5x+10=110`

`5x=100`

`x = 20`

of course, `x` is the first integer in the sequence, so the fourth number is:

`x+3 = 23`

Answer 2

See explanation.

Explanation:

The 5 consecutive integers can be expressed as:

`x`, `x+1`, `x+2`, `x+3` and `x+4`. If we write their sum as an expression we get:

`5x+10`

If we solve the equation we get:

`5x+10=110=>5x=100=>x=20`

Now the fourth term in the sequence is: `x+3=23`

Answer 3

I prefer to name my variables starting in the middle.

Explanation:

`n` is the middle number.

The two less than `n` are `n-1` and `n-2`

The two numbers greater than `n` are `n+1` and `n+2`.

The sum is `(n-2)+(n-1)+n+(n+1)+(n+2) = 5n = 110`

So `n = 110/5 = 22`

The fourth number is `n+1 = 22+1=23`