Question

Melissa exercises for 20 minutes every day to decide to increase her daily exercise Time by 5 minutes each week however according to her doctor's orders she could spend no more than 45 minutes a day exercise how many weeks can Melissa increase your exercise time this way ​

Answer 1

Step-by-step explanation:

The stated problem is of Arithmetic progression, where: $a_1=20,\:\:d = 5\\:\: t_n=45 \:\: \&\:\: n=?$

By nth term of an AP we have:

$t_n = a + (n - 1)d \\ \\ \therefore \: 45 = 20 + (n - 1) \times 5\\ \\ \therefore \: 45 - 20 = (n - 1) \times 5 \\ \therefore \: 25 = 5n - 5\\ \\ \therefore \: 25 + 5 = 5n \\ \\ \therefore \: 30= 5n \\ \\ \therefore \: n = \frac{30}{5} \\ \\ \huge \red{ \boxed{\therefore \: n =6}}$