Question

nevaeh opened a savings account at week 0 with $1,200 that pays no interest. she deposits an additional $160 each week thereafter. how much money would nevaeh have in the account 30 weeks after opening the account?

Explanation:

Step1: Identify the formula type

This is an arithmetic sequence problem where the initial amount (a₀) is $1200, the common difference (d) is $160 per week, and we need to find the amount at week n = 30. The formula for the amount after n weeks is \( A(n)=a_0 + n\times d \) (since at week 0, n=0, and each week we add d, so after n weeks, we've added n times d).

Step2: Plug in the values

Here, \( a_0 = 1200 \), \( d = 160 \), and \( n = 30 \). So we calculate \( A(30)=1200 + 30\times160 \).
First, calculate \( 30\times160 = 4800 \).
Then, add the initial amount: \( 1200+4800 = 6000 \).

Answer:

\$6000