Question

Mangala started doing physical exercise 10 minutes for the first day. She will increase the time of exercise by 5 minutes per day, till she reaches 45 minutes per day. How many days are required to reach 45 minutes?

Answer 1

Because the physical exercise time is 10 minutes for the first day and it is increased by 5 minutes per day, the exercise times are in an A.P.
Here,
First term, a = 10
Common difference, d = 5
Let the exercise time become 45 minutes per day after n days.
Now, we have:
t_n = 45
We need to find the value of n.
We know that the n^th term of an A.P. is t_n = a + (n – 1)d.
By taking a = 10, d = 5 and t_n = 45, we get:
45 = 10 + (n – 1)5
$\Rightarrow$45 – 10 = 5n –5
$\Rightarrow$35 = 5n –5
$\Rightarrow$5n = 35 + 5 = 40
$\Rightarrow$n = $\frac{40}{5}$ = 8
Thus, the exercise time becomes 45 minutes per day after 8 days.