A toy model manufacturing company is going to start work on a new model boat design. The company plans to produce 62 units in its first week and then increase production by 75 units each week for all future weeks. The total number of manufactured model boats can be modeled with the arithmetic sequence 62, 137, 212, 287, . . . . Following this sequence, how many model boats would be manufactured in the 12th week?(1 point)

Question

The company could manufacture
model boats in the 12th week.

Answer 1

To find out how many model boats would be manufactured in the 12th week, we start with the arithmetic sequence given by:

• First term (a) = 62 (the number produced in the first week)
• Common difference (d) = 75 (the increase in production each week)

The formula for the nth term of an arithmetic sequence is given by:

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

where:

• \( a_n \) is the nth term
• \( a \) is the first term
• \( n \) is the term number
• \( d \) is the common difference

For the 12th week (n = 12), we can substitute the values into the formula:

\[ a_{12} = 62 + (12 - 1) \times 75 \] \[ a_{12} = 62 + 11 \times 75 \] \[ a_{12} = 62 + 825 \] \[ a_{12} = 887 \]

So, the company could manufacture 887 model boats in the 12th week.