# Greta is opening a savings account. She starts with $100 and plans to add$50 each week. How do you write an equation she can use to calculate the amount of money she will have after any number of weeks. How much money will she have after 1 year?

Greta will have color(blue)($2,700 after one year in her savings account. #### Explanation: Initial deposit a =$ 100
Deposited after one week d = $50 Amount after one week A^_1 = a + d = 100 + 50 =$ 150
Amount after two weeks A_2 = A_1 + d = (a + d) + d = a + 2d = 100 + (2 * 50) = $200 Similarly after three weeks, ${A}_{3} = \left(a + 2 d\right) + d = a + 3 d$Hence after n number of weeks, ${A}_{n} = a + n d$In a year, there are 52 weeks. Thus after one year ( or 52 weeks), A_(52) = a + (52 * d) = 100 + (52 * 50) = 100 + 2600 =color(blue)($ 2,700