The nth term of an arithmetic series is given by the formula t(n)=42+12(n-1).
A
a
See solution.
B
b
960, see solution.
C
c
36n+6n^2
Practice makes perfect
a
The difference between a sequence and a series is that a sequence a_n is an ordered list of numbers, while a series S_n is the sequence of cumulative sums of those numbers.
In our case, the sequence corresponds to the list of the class sizes of the graduating classes in a particular year. The corresponding series represents the total number of graduating students in each year.
t(n)=42+12(n-1)
Therefore, to calculate the total number of graduates after the 10th graduation, we can use the following formula for the sum of an arithmetic series.
S_n=n(t_1+t_n)/2
To use this formula we need to know the first and last term of the series. We can find the first term by substituting n=1 into the formula.
After the 10th graduation ceremony there were t_(10)=150 graduates and that after the 1st ceremony there were t_1 =42 graduates. Now we can determine how many total graduates there should be.
The number of graduates after n years is represented by the following formula.
t(n)=42+12(n-1)
Let's use the same formula as in Part B. If we substitute the equation above into this formula, we get a general equation for the number of invitations they have to make.
