Question

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

Answer 1

Answer:  The correct option is

(C) 26.

Step-by-step explanation: Given that in a certain quiz that consists of  10 questions, each question after the first is worth 4 points more than the preceding question.

All  the 10 questions on the quiz are worth a total of 360 points.

We are to find the worth of the third question in points.

Since each question after the first is worth 4 points more than the preceding question, so this will make an arithmetic sequence with

first term a, common difference, d = 4  and number of terms, n = 10.

We know that, in an A.P. with first term a and common difference d,

$\textup{nth term, }a_n=a+(n-1)d,\\\\\textup{sum of first n terms, }S_n=\dfrac{n}{2}\{2a+(n-1)d\}.$

According to the given information,

$\textup{sum of first 10 terms, }S_n=360\\\\\Rightarrow \dfrac{10}{2}\{2a+(10-1)4\}=360\\\\\Rightarrow 5(2a+36)=360\\\\\Rightarrow 10(a+18)=360\\\\\Rightarrow a+18=36\\\\\Rightarrow a=36-18\\\\\Rightarrow a=18.$

Therefore, the third term of the sequence is

$a_3=a+(3-1)d=18+2\times4=18+8=26.$

Thus, the third question worth 26 points.

Option (C) is CORRECT.