Question 85945
First year tuition = $6500
Second year tuition = $6500 + $750 = $7250
Third year tuition = $7250 + $750 = $8000
Fourth year tuition = $8000 + $750 = $8750
Graduation
(a) She should expect to pay $8750 for her fourth year tuition.
(b) The total tuition she will pay is $6500 + $7250 + $8000 + 8750 = $30,500
.
You might notice that this is an arithmetic progression. The first term (call it "a") is
$6500.  The common difference between terms (call it "d") is $750. The number of terms in
the progression (call it "n") is 4, and the last term (call it "L") is 4.
.
The last term in an arithmetic progression is given by the equation:
.
L = a + (n-1)*d
.
Substitute the known values for a, n, and d to get:
.
L = $6500 + (4-1)*$750 = $6500 + 3*$750 = $6500 + $2250 = $8750
.
Notice that this is the answer to question (a) above.  She should expect to pay $8750 in
tuition for her last year.
.
The sum (call it "S")of a finite number of terms in an arithmetic progression is given by 
the equation:
.
{{{S = (n*(2a + (n-1)*d))/2}}}
.
Substitute the values of a, d, and n for this problem and the sum becomes:
.
{{{S=(4*((2*6500)+(4-1)*750))/2=(4*(13000+3*(750)))/2=(4*(13000+2250))/2=(4*15250)/2 = 61000/2=30500}}}
.
So using the equation for the sum you can find the total paid for the four years of tuition
is $30,500 ... the same as we calculated previously.
.
Hope this helps you to understand arithmetic progressions and the equations for finding the
last term and the sum of the terms.