Question

An adult dose of niacin is initially 250 mg/day. This is increased every week for 11 weeks until a maintenance dose of 3000 mg/day is reached. What is the increase in dosage per week?

Answer 1

1. Starting dose for niacin  = 250 mg/day
2. Maintenance dose to be reached = 3000 mg/day...... (1)
3. The dose has to be increased by a constants amount over 11 weeks. In other words, weekly increments have to be constant.
4. The dose in the first week = 250 mg
5. The dose in the 2nd week = (Dose of first week)+ x = 250 + x
6. The dose in the 3rd week = (Dose of 2nd week) + x = 250 + 2x
7. The dose in the 4 th week = (dose of 3rd week) + x = 250 + 3x
8. The dose in the 5 th week = (dose of 4th week) + x = 250 +4x
9. The dose in the 6 th week = (dose of 5th week) + x = 250 +5x
10. The dose in the 7 th week = (dose of 6th week) + x = 250 +6x
11. The dose in the 8 th week = (dose of 7th week) + x = 250 +7x
12. The dose in the 9 th week = (dose of 8th week) + x = 250 +8x
13. The dose in the 10 th week = (dose of 9th week) + x = 250 +9x
14. The dose in the 11 th week = (dose of 10th week) + x = 250 +10x
15. So, the dose at the end of 11 weeks = 250 + 10x, but the final dose at the end of 11 weeks should be 3000mg
16. Therefore, 250 + 10x = 3000
17. 10x = 2750
18. x = 275
19. So the the weekly increments in the dose should be 275 mg to reach a total dose of 3000
20. The formula is .... a + (n-1)c = A --------- (2)
    1. Where a = initial dose ( in this problem it is 250 mg)
    2. Where n = total duration ( in this problem it is 11 weeks)
    3. Where c = the constant increment in the dose ( In this problem it is 275 mg)
    4. Where A = the final dose ( in this equation it is 3000mg)

Now let us confirm the formula by putting the value

• Formula = a + (n-1)c =A
• let us insert the values
• 250 + (11 -1) 275
• 250 + 10 * 275
• 250 + 2750
• 3000.

The final answer is the dose of niacin should be increased by 275 mg per week for 11 weeks to reach a dose of 3000mg