Question

Sheila decides to embark on a swimming program as the best way to maintain cardiovascular health. She begins by swimming 5 min on the first day, then adds 1 1/2 min every day after that. Find a recursive formula for the number of minutes Tₙ that she swims on the n th day of her program.

Answer 1

The recursive formula for the number of minutes Sheila swims on the nth day of her program is Tn = Tn-1 + 1 1/2

Step-by-step explanation:

To find a recursive formula for the number of minutes Sheila swims on the nth day of her program, we can observe the pattern of her swim times. On the first day, she swims for 5 minutes. On the second day, she swims for 5 + 11/2 minutes. On the third day, she swims for (5 + 11/2) + 11/2 minutes. This pattern continues, with each day's swim time being the previous day's swim time plus 11/2 minutes. Therefore, the recursive formula for the number of minutes Tn that she swims on the nth day is:

Tn = Tn-1 + 11/2