In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 360 points, how many points is the third question worth?
A. 18
B. 24
C. 26
D. 32
E. 44
Is there a strategic approach to this question? Any experts help please?
Hi ardz24,
Let's take a look at your question.
Each question after the first is worth 4 points more than the preceding question, so we can write the sequence of points as:
x, x+4, x+8, x+12, ... x+36 (10 questions total)
This seems to be an arithmetic sequence with:
$$n=10,\ d=4$$
The 10 questions on the quiz are worth a total of 360 points, which represents that the sum of 10 terms of the arithmetic sequence is 360, i.e.
$$S=360$$
We know that the sum of the arithmetic sequence can be represented using the formula:
$$S=\frac{n}{2}\left[2a_1+\left(n-1\right)d\right]$$
$$360=\frac{10}{2}\left[2a_1+\left(10-1\right)4\right]$$
$$360=5\left[2a_1+\left(9\right)4\right]$$
$$360=5\left[2a_1+36\right]$$
$$\frac{360}{5}=\left[2a_1+36\right]$$
$$72=\left[2a_1+36\right]$$
$$2a_1=72-36$$
$$2a_1=36$$
$$a_1=\frac{36}{2}=18$$
a1 represents the first term in the sequence, i.e. points of the first question.
Points of second question = 18 + 4 = 22
Points of the third question = 22 + 4 = 26
Therefore Option
C is correct.
Hope it helps.
I am available if you'd like any follow up.
