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13 problems match “arithmetic sequences”. Clear

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.
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?
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.
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 $q$ .
Smallest average of distinct even integers ●○○○○ 10 ptsWhat is the smallest possible average of four distinct positive even integers?
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 $a_1 + a_2 + \dots + a_{100}$ ?
Maximum leap years in 150 years ●●○○○ 20 ptsIn a calendar system in which leap years occur every four years, with no exceptions, what is the maximum possible number of leap years in a 150-year period?
Alternating sum in steps of four ●●○○○ 20 ptsFind the value of $2013-2009+2005-2001+\cdots+29-25$ .
Corrected value in a quadratic table ●●○○○ 20 ptsA student plots $y=ax^2+bx+c$ ( $a\neq 0$ ) using seven equally spaced $x$ -values $x_1<x_2<\cdots<x_7$ , where $x_{k+1}-x_k$ is constant. The recorded $y$ -values are $51, 107, 185, 285, 407, 549, 717$ for $x_1,\ldots,x_7$ respectively. Exactly one of these $y$ -values was calculated incorrectly. Find the correct value of that $y$ -value.
Sum of alternate terms of a sequence ●●●○○ 50 ptsA sequence consists of 2010 terms. Each term after the first is 1 larger than the previous term. The sum of the 2010 terms is 5307. When every second term is added up, starting with the first term and ending with the second last term, what is the sum?