^{40}/

_{5}

3. 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. How many days are required to reach 45 minutes?

Sol. Since the workout time Mangala increases by 5 minutes everyday after the first day, the successive workout times are in A.P.

Workout time for first day (a) = 10 minutes.

Increases in workout time (d) = 5 minutes

Let No. of days required to reach workout time of 45 minutes be ‘n’ days.

∴ tn = 45

tn = a + (n – 1) d

∴ 45 = 10 + (n – 1) 5

∴ 45 = 10 + 5n – 5

∴ 45 = 5 + 5n

∴ 45 – 5 = 5n

∴ 5n = 40

∴ n = ^{40}/_{5}

∴ n = 8

∴ 8 days required to reach work out time of 45 minutes.