115. sami opens an account and deposits $100 into it at the end of each month. the account earns 2% per year compounded monthly. let sn denote the amount of money in her account at the end of n months (just after she makes a deposit). for example, s1 = 100 and s2 = 100(1 + 0.02 /12)+100
a. write a geometric series for the amount of money in the account after 3, 4, and 5 months.

Step-by-step explanation:

Geometric series.

Month 3.

      100(1+\frac{0.02}{12})^2 + 100(1+\frac{0.02}{12})+100

Month 4.

100( 1 + \frac{0.02}{12})^3 + 100( 1 + \frac{0.02}{12})^2+100(1+\frac{0.02}{12})+100

Month 5.

100(1 + \frac{0.02}{12})^4 + 100(1 + \frac{0.02}{12})^3 + 100(1 + \frac{0.02}{12})^2 +100( 1 + \frac{0.02}{12}) + 100

answer: 42

use a calculator to find that 845/73 = 11.575

the whole part of the answer is 11. multiply this by 73 to get 11*73 = 803.

subtract that result from 845 to get 845 - 803 = 42

cross multiplying, we get :

⇒ (3) × (5) = (9) × (x)

⇒ 15 = 9x