Question

A sebastian le encargan suministrar la dosis de un medicamento.El primer dia la dosis debe ser de 100 miligramos y sera 5 miligramos menos cada uno de los siguientes dias . El tratamiento dura 12 dias¿ cuantos miligramos tiene que tomar el enfermo durante todo el tratamiento

Answer 1

The patient took 1,530 milligrams during the complete treatment.

Explanation:

This problem is about arithmetic sequence, where the difference is 5, that is, the sequence is formed by summing 5 to each term. We know that the first day, the dosis should be 100 milligrams, starting from that we form the sequence

`100,105,110,115,120,125,130,135,140,145,150,155`

However, the question is about the total milligrams the person took during all treatment. We can find the sum of all terms with the following formula.

`S_(n)=(n(a_(1)+a_(n) ))/(2)`

Where
`a_(1)=100`,
`n=12` and
`a_(n)=a_(12)=155`. Replacing these values, we have

`S_(12)=(12(100+155))/(2)= 1,530`

Therefore, the patient took 1,530 milligrams during the complete treatment.