Question

Shannon started a savings account by putting in $25. On the 1st week shedeposited $15 and plans to continue depositing $15 each week.What is the recursive formula for the sequence represented by Shannon'sdeposits.

Answer 1

We have a sequence where we know that the initial term a0 is 25.

`a_0=25`

Then, each term adds the common difference of 15, so we can write:

`a_n=a_(n-1)+15`

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:

`\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}`

Then, the explicit formula is a(n) = 25 + 15n.

Answer:

Recursive formula: a(n) = a(n-1) + 15

Explicit formula: a(n) = 25 + 15n