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.