Question

Steven deposits $200 in a savings account, and decides to increase the amount by $5 every month. Identify the function that describes the arithmetic sequence, and the amount he should deposit after 8 months.

Answer 1

To describe the deposits Steven makes, we can define it as an arithmetic sequence.

An arithmetic sequence is defined by a first term and a common difference.

In this case:

- The first term, \( a_1 \), is the initial deposit, which is \( 200 \) dollars.
- The common difference, \( d \), is the increase in deposit each month, which is \( 5 \) dollars.

The general formula for the \( n \)-th term \( a_n \) of an arithmetic sequence can be given by:

\[
a_n = a_1 + (n-1) \times d
\]

Plugging in the values we have:

\[
a_n = 200 + (n-1) \times 5
\]

To find out how much he should deposit after 8 months, we need to find \( a_8 \):

\[
a_8 = 200 + (8-1) \times 5
\]
\[
= 200 + 7 \times 5
\]
\[
= 200 + 35
\]
\[
= 235
\]

Thus, after 8 months, Steven should deposit **$235**.