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.