Respuesta :
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,
[tex]\textup{nth term, }a_n=a+(n-1)d,\\\\\textup{sum of first n terms, }S_n=\dfrac{n}{2}\{2a+(n-1)d\}.[/tex]
According to the given information,
[tex]\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.[/tex]
Therefore, the third term of the sequence is
[tex]a_3=a+(3-1)d=18+2\times4=18+8=26.[/tex]
Thus, the third question worth 26 points.
Option (C) is CORRECT.
