A boat manufacturing company is going to start work on a new boat design. The company plans to produce 62 units in its first week and then increase production to 75 units for all future weeks. The total number of manufactured boats can be modeled with the arithmetic sequence 62, 137, 212, 287, . . . . How many boats could be manufactured in the 12th week?(1 point)%0D%0AThe company could manufacture boats in the 12th week.
The pattern of production can be seen as an arithmetic sequence where each term is 75 more than the previous term.
To find how many boats could be manufactured in the 12th week, we need to find the 12th term of the arithmetic sequence.
The formula to find the nth term of an arithmetic sequence is:
an = a1 + (n-1)d
Where:
an = the nth term
a1 = the first term
d = the common difference
In this case:
a1 = 62
d = 75 - 62 = 13
Plugging in the values:
a12 = 62 + (12-1) * 13
a12 = 62 + 11 * 13
a12 = 62 + 143
a12 = 205
Therefore, the company could manufacture 205 boats in the 12th week.