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1. Arithmetic sequence of pentagon angles ●○○○○ 10 ptsLet $v$, $w$, $x$, $y$, and $z$ be the degree measures of the five angles of a pentagon. Suppose $v<w<x<y<z$ and $v$, $w$, $x$, $y$, $z$ form an arithmetic sequence. Find the value of $x$ in degrees.
2. Next term of a fraction sequence ●○○○○ 10 ptsFind the next term of the sequence $0, 0.5, 0.\overline{6}, 0.75, \dots$ and give it as a decimal. Round to three decimal places.
3. Shared sale dates in July ●○○○○ 10 ptsA bookstore has a sale on days of the month that are multiples of 5 (such as June 5, June 10, ...). A shoe store has a sale every 6 days. The shoe store has a sale on July 3. How many times in July do the two stores have sales on the same date?
4. Hundredth term of a fraction sequence ●○○○○ 10 ptsThe sequence $\frac{1}{2}, \frac{3}{5}, \frac{5}{8}, \frac{7}{11}, \frac{9}{14}, \ldots$ follows a pattern. Find the 100th term of the sequence. Round your answer to two decimal places.
5. Fifth term of a recursive sequence ●○○○○ 10 ptsIn the sequence $\{a_n\}$, $a_1=2$ and $a_{n+1}=2a_n-1$. Find $a_5$.
6. Common ratio from an arithmetic condition ●○○○○ 10 ptsFor a geometric sequence $\{a_n\}$ with sum of the first $n$ terms $S_n$, we have $a_1=1$, and $a_1$, $S_2$, $5$ (in this order) form an arithmetic sequence. Find the common ratio $q$.
7. Smallest average of distinct even integers ●○○○○ 10 ptsWhat is the smallest possible average of four distinct positive even integers?
8. Sum after repeated difference insertion ●●○○○ 20 ptsWrite the 4 numbers $1,9,8,8$ in a row and perform the following operation: for each pair of adjacent numbers, subtract the left number from the right number, and write the result between the two numbers. This completes one operation. Then perform the same operation on the 7 numbers now in a row, and continue this process for a total of 100 operations. Find the sum of the final row of numbers.
9. Least difference between geometric and arithmetic terms ●●○○○ 20 ptsSequence $A$ is a geometric sequence and sequence $B$ is an arithmetic sequence. Each sequence stops as soon as one of its terms is greater than $300$. Sequence $A$: $2, 4, 8, 16, 32, \ldots$. Sequence $B$: $20, 40, 60, 80, 100, \ldots$. Find the least positive difference between a number selected from sequence $A$ and a number selected from sequence $B$.
10. Alternating sum of a linear sequence ●●○○○ 20 ptsThe $n$th term of a sequence is $a_n = (-1)^{n+1}(3n + 2)$. What is the value of $a_1 + a_2 + \dots + a_{100}$?

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