Question

The sum of four consecutive integers is 38. What is the value of the secondnumber in the sequence

Answer 1

The sum of four consecutive integers is 38.

Let the 1st integer be x

Then the 2nd integer will be x + 1

Then the 3rd integer will be x + 2

Then the 4th integer will be x + 3

Now, let us add these integers and equate the sum to 38.

`x+(x+1)+(x+2)+(x+3)=38`

Let us solve the equation for x.

`\begin{gathered} x+x+1+x+2+x+3=38 \\ x+x+x+x+1+2+3=38 \\ 4x+6=38 \\ 4x=38-6 \\ 4x=32 \\ x=(32)/(4) \\ x=8 \end{gathered}`

So, the 1st integer is 8

The second integer is (x+1) = 8+1 = 9

The sequence is 8, 9, 10, 11