Select all the correct answers. sophia has a book fund to save money for her college textbooks, and she also works at a part-time job. sophia's grandmother has given her $1,000 to start the fund. since sophia is working, she also adds $50 to the fund each month from the money she earns. select all the functions that can be used to find the total amount of money, f(n), in the college book fund after n months.

f(n)=50n+950

f(1)=1,000; f(n)=f(n-1)+50, for n≥2

Step-by-step explanation:

Sophia's grandmother gave her $1,000 to start the book fund. Sophia decided to add $50 to the fund each month from the money she earns.

Since Sophia adds a fixed amount to the college fund each month, the situation represents an arithmetic sequence with a common difference of 50.

If a is the initial value of the arithmetic sequence and d is the common difference, the explicit function below can be used to write the function.

f(n)=a+(n-1)d

Substitute a = 1,000 and d = 50 in the explicit function above and simplify.

f(n)=a+(n-1)d

f(n)=1,000+(n-1)50

f(n)=1,000+50n-50

f(n)=50n+950

So, the explicit formula that can be used to define the given situation is f(n) = 50n + 950.

Recall the recursive form of an arithmetic sequence, where d is the common difference.

f(n)=f(n-1)+d, for n≥2

For the recursive formula, the first term of the sequence, f(1), must be known. For the given situation, f(1) = 1,000.

To determine the recursive formula for the situation, define the first term, f(1) = 1,000 and substitute d = 50 into the recursive form of an arithmetic sequence as shown below.

f(1)=1,000

f(n)=f(n-1)+50, for n≥2