Practice Solving Consecutive Integer Problems

Call the first number in the sequence $$x$$.

The next odd number in the sequence is $$x+2$$.

The sum of the 5 consecutive odd numbers is:

$$x+ (x + 2)+ (x + 4)+ (x + 6)+ (x + 8) = 135$$

$$5x + 20= 135$$

$$5x = 115$$

$$x = 23$$

Since $$x$$ is the first number, $$x+2$$ is the second odd number.

Thus, the second number in the sequence is 25.

Call the first number in the sequence $$x$$.

The next integer in the sequence is $$x+1$$

The sum of the 6 consecutive integers is:

$$x+ (x + 1)+ (x + 2)+ (x + 3)+ (x + 4)+ (x + 5) = 393$$

$$6x + 15= 393$$

$$6x = 378$$

$$x = 63$$

Since $$x$$ is the first number, $$x+2$$ is the third integer.

Thus, the third number in the sequence is 65.

Call the first number in the sequence $$x$$.

The next integer in the sequence is $$x+2$$

The sum of the 3 consecutive even numbers is:

$$x+ (x + 2)+ (x + 4) = 270$$

$$3x + 6= 270$$

$$3x = 264$$

$$x = 88$$

Thus, the first number is 88.

Call the first number in the sequence $$x$$.

The next integer in the sequence is $$x+1$$

The sum of the 4 consecutive integers is:

$$x+ (x + 1)+ (x + 2)+ (x + 3) = 326$$

$$4x + 6= 326$$

$$4x = 320$$

$$x = 80$$

Since $$x$$ is the first number, $$x+1$$ is the third integer.

Thus, the third number in the sequence is 81.