Question

Suppose you have $50 in a savings account and deposit an additional $10 each week.

a) Write a recursive formula to represent the sequence.
b) Write an explicit formula to represent the sequence.
c) How much money do you have in savings after 26
weeks? Show all work.​

Answer 1

The recursive formula for the sequence is an = an-1 + 10, the explicit formula is an = 50 + 10(n-1), and after 26 weeks, the amount of money in savings would be $300.

Step-by-step explanation:

a) The recursive formula to represent the sequence is: an = an-1 + 10. This means that each term in the sequence is obtained by adding 10 to the previous term.

b) The explicit formula to represent the sequence is: an = 50 + 10(n-1). This means that each term in the sequence is obtained by adding 10 times the position of the term in the sequence to 50.

c) To find the amount of money in savings after 26 weeks, plug in n=26 into the explicit formula: a26 = 50 + 10(26-1) = 50 + 10(25) = 300. Therefore, after 26 weeks, you would have $300 in savings.