Final answer:
The possible value for the first integer in a sequence of three consecutive integers whose sum is between 51 and 72 can range from 16 to 23.
Step-by-step explanation:
A student has asked for the possible value of the first integer when three consecutive integers have a sum that is between 51 and 72. To solve this, we can let the first integer be x, the second integer be x + 1, and the third integer be x + 2.
The sum of these three integers can be expressed as x + (x + 1) + (x + 2), which simplifies to 3x + 3. We are given that 51 ≤ 3x + 3 ≤ 72. Solving these inequalities for x, we subtract 3 from all parts of the inequality, yielding 48 ≤ 3x ≤ 69. Finally, we divide all parts by 3 to isolate x, resulting in 16 ≤ x ≤ 23. So the possible values for the first integer are 16, 17, 18, 19, 20, 21, 22, and 23.