We have a sequence where we know that the initial term a0 is 25.
[tex]a_0=25[/tex]
Then, each term adds the common difference of 15, so we can write:
[tex]a_n=a_{n-1}+15[/tex]
The recursive formula for this sequence, representing how much she has in her savings account, is a(n) = a(n-1) + 15.
To find the explicit formula, we relate each term to the first term in order to find the relation:
[tex]\begin{gathered} a_1=a_0+15=25+15 \\ a_2=a_1+15=(25+15)+15=25+2\cdot15 \\ a_n=25+n\cdot15=25+15n_{} \end{gathered}[/tex]
Then, the explicit formula is a(n) = 25 + 15n.
Answer:
Recursive formula: a(n) = a(n-1) + 15
Explicit formula: a(n) = 25 + 15n
