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?

Answer 1

Explanation:

Given that each question after the first is worth 4 points more than the preceding question.

Total questions = 10

Let a be the marks for the first question.

Then the marks for 10 questions in order are a, a+4, a+8,....a+36

This is an arithmetic sequence with common difference d =4

Sum of 10 terms =
`S_(10) =(10)/(2) (2a+36)\\=10a+180`

This sum is given as 360

Equating we get

`10a+180 =360\\a = 18`

Hence III question will have points as 18+2(4) = 26.