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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?

Respuesta :

Answer:

Step-by-step 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 =[tex]S_{10} =\frac{10}{2} (2a+36)\\=10a+180[/tex]

This sum is given as 360

Equating we get

[tex]10a+180 =360\\a = 18[/tex]

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