Question 7

Explanation

Determining the Common Difference

January is the first month ($U_1$), so the number of cars produced is $a = 100$ units. April is the 4th month ($U_4$), with a production of $160$ units.

We can find the common difference ($b$) of this arithmetic sequence using the $n$-th term formula:

Substitute the known values for April ($n=4$):

So, production increases by $20$ units each month.

Calculating Total Annual Production

Total production until the end of the year means the sum of production for $12$ months ($S_{12}$). We use the arithmetic series sum formula:

Substitute $n = 12$, $a = 100$, and $b = 20$:

Thus, the total number of cars that can be produced by the end of the year is $2,520$ units.