The problem describes a linear decrease in sputum volume, which means it follows an arithmetic progression.

Right Abba, let's go. The problem describes a linear decrease in sputum volume, which means it follows an arithmetic progression. Step 1: Identify the given values. The initial volume on day 1 (a_1) is 45 ml. The final volume on day 7 (a_7) is 15 ml. The total number of days (n) is 7. We need to find the volume on the middle day. Step 2: Calculate the common daily decrease (d). The formula for the n-th term of an arithmetic progression is a_n = a_1 + (n-1)d. Using a_7 = 15 ml and a_1 = 45 ml: 15 = 45 + (7-1)d 15 = 45 + 6d Subtract 45 from both sides: 15 - 45 = 6d -30 = 6d Divide by 6: d = (-30)/(6) d = -5 ml/day The sputum volume decreases by 5 ml each day. Step 3: Determine the middle day. For a period of 7 days, the middle day is the (7+1)/(2)-th day, which is the 4-th day. So we need to find a_4. Step 4: Calculate the sputum volume on the middle day (a_4). Using the formula a_n = a_1 + (n-1)d for n=4: a_4 = a_1 + (4-1)d a_4 = 45 + (3)(-5) a_4 = 45 - 15 a_4 = 30 ml The middle value is the sputum volume on day 4. The middle value is 30 ml. Send me the next one 📸