To find the second number in a sequence of 5 consecutive integers whose sum is 270, we can start by letting the first integer be represented by the variable x. The five consecutive integers can then be expressed as:
- x (1st integer)
- x + 1 (2nd integer)
- x + 2 (3rd integer)
- x + 3 (4th integer)
- x + 4 (5th integer)
The sum of these five integers can be set up in an equation:
x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 270
This simplifies to:
5x + 10 = 270
Next, we can solve for x. Subtract 10 from both sides:
5x = 260
Now, divide by 5:
x = 52
Now that we have the first integer, we can determine the second integer:
x + 1 = 52 + 1 = 53
Therefore, the second number in this sequence of 5 consecutive integers is 53.