Question

Jessica had $150 in her savings account on the first Sunday of November. Beginning this that week, she say $35 each week. Write a recursive rule that describes how much money Jessica Addie her savings account at the end of n weeks.

Answer 1

Hey there!

$150 is the amount that Jessica is starting with. That means that the first term, or a₁, will be 150. As the weeks progress, $35 dollars will be added on top of the amount from the previous week. That means that your recursive rule will be:

$a_{1} = 150; a_{n} = a_{n-1}+35$

If you wanted to check this, you could plug in the data for each week, starting with 2 (since we already know week 1). 

$a_{1} = 150; a_{n} = a_{n-1}+35$
$a_{1} = 150; a_{2} = a_{1}+35$
$a_{1} = 150; a_{2} = 150+35$
$a_{1} = 150; a_{2} = 185$

Hope this helped you out! :-)