Question

On Gabriela’s first birthday, her parents gave her a $50 savings account. On every birthday after that her parents added to the account, increasing the amount they deposited by $25 each year. Complete the recursive definition for the sequence that represents this situation by finding the values for a1 and d. Calculate the total amount Gabriela’s parents will have deposited into the account on her birthdays by her 18th birthday.

Answer 1

Answer: $a_1=50,d=25$ and $475 deposited into the account on her birthdays by her 18th birthday.

Step-by-step explanation:

It is given that, on Gabriela’s first birthday, her parents gave her a $50 savings account.

Initial term : $a_1=50$

On every birthday after that her parents added to the account, increasing the amount they deposited by $25 each year.

Common difference : $d=25$

It forms an AP: 50,75,100,...

nth term of an AP is

$a_n=a_1+(n-1)d$

Substitute $a_1=50$ and $d=25$ in the above formula.

$a_n=50+(n-1)25$

It represents the amount deposited into the account after n birthdays.

We need to find the amount by her 18th birthday.

Put n=18 in the above equation.

$a_{18}=50+(18-1)25$

$a_{18}=50+(17)25$

$a_{18}=50+425$

$a_{18}=475$

Therefore, $475 deposited into the account on her birthdays by her 18th birthday.