a Let's write an expression for the given arithmetic sequence. We can start by finding the common difference. To do so we will subtract consecutive terms.
We found the formula of our arithmetic sequence. The grade of the student on his sixth test is the sixth term of the arithmetic sequence. To find its value, we will substitute 6 for n in the obtained formula.
If the student continues to improve at the same rate, the sixth test will have a score of 95.
b Let's use the formula for the sum of a finite arithmetic series to find the sum of our series. First, we can set up our summation for the six tests using the formula we derived from Part A.
S_6= ∑_(n=1)^6 (71+4n)
We know the first term is a_1 = 75, the last term is a_6 = 95, and that the series has 6 terms. Let's substitute these values into the sum formula to find the sum of the six terms in the series.
