Question

Jobie starts with $325 in her piggy bank. Each month she adds $10. Which recursive function rule models the total amount in Jobie's piggy bank at the end of each month? hint recursive formula for arithmetic functions is an an-1 +d

Answer 1

A₀ = 325, initial amount
a₁ = 325 + 10 = a₀ + 10, after 1 month
a₂ = a₁ + 10, after 2 months

After n months,
$a_{n} = a_{n-1} +10$

Answer:
he recursive formula is
$a_{n} = a_{n-1} + 10, \, n=1,2, \, ..., \\ where \, a_{0}=325$

Answer 2

This is the concept of arithmetic sequence. To get the recursive formula that models the total amount Jobie has in her account we use the arithmetic formula given by:
an=a+(n-1)d
where:
an=nth term
a=first term
n=number of terms
d=arithmetic difference
in our case
a=$325
d=$10
the initial amount was:
a0=325
the amount in the second month will be:
a1=325+10
the amount in the thrid month will be:
a2=a1+10
after n months the we shall have:
an=a_(n-1)+10
hence the recursive formula will be:
an=a_(n-1)+10
where:
n=1,2,3,4,...,
a0=325