Arithmetic Progressions

Arithmetic Mean

What is the arithmetic mean of $3a +15$ and $7a -9$ ?

10a+6

5a+3

5a+7

10a+3

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by Brilliant Staff

$8, x, 16, 18$

If the average of the above numbers is 13, what is $x$ ?

11 10 13 12

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What is the arithmetic mean of all the prime numbers less than 20?

\frac{92}{9}

\frac{77}{8}

\frac{75}{8}

\frac{58}{7}

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What is the arithmetic mean of all the leap years in the $19^{\text{th}}$ century?

Details and Assumptions:
A year that is divisible by 4 is a leap year. However, a year that is divisible by 100 but not by 400 is a common year.

The $19^{\text{th}}$ begins with January 1, 1801 and ends with December 31, 1900.

1848 1851 1850 1852

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$-10, -6, -2, 2, 6, 10$ What is the arithmetic mean of the above sequence?

-2 2 0

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