Missing Terms in Sequences - ISEE Upper Level: Quantitative Reasoning
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What is the missing term in the sequence $3, 7, 13, 21, _, 43$ where each term is $n^2+n+1$?
What is the missing term in the sequence $3, 7, 13, 21, _, 43$ where each term is $n^2+n+1$?
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$31$. Each term follows the pattern $n^2 + n + 1$ for consecutive integers n starting from 1, so use n=5.
$31$. Each term follows the pattern $n^2 + n + 1$ for consecutive integers n starting from 1, so use n=5.
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What is the missing term in the sequence $2, 5, 10, 17, _, 37$ where each term is $n^2+1$?
What is the missing term in the sequence $2, 5, 10, 17, _, 37$ where each term is $n^2+1$?
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$26$. Each term follows the pattern $n^2 + 1$ for consecutive integers n starting from 1, so use n=5.
$26$. Each term follows the pattern $n^2 + 1$ for consecutive integers n starting from 1, so use n=5.
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What is the missing term in the sequence $1, 2, 6, 24, _, 720$?
What is the missing term in the sequence $1, 2, 6, 24, _, 720$?
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$120$. This sequence follows the factorial pattern $n!$, so the fifth term is $5!$.
$120$. This sequence follows the factorial pattern $n!$, so the fifth term is $5!$.
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What is the missing term in the sequence $2, 3, 5, 8, 12, _, 23$ where differences increase by $1$?
What is the missing term in the sequence $2, 3, 5, 8, 12, _, 23$ where differences increase by $1$?
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$17$. Differences increase by 1 starting from 1, so add 5 to 12 to find the missing term.
$17$. Differences increase by 1 starting from 1, so add 5 to 12 to find the missing term.
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What is the missing term in the geometric sequence $81, 27, 9, _, 1$?
What is the missing term in the geometric sequence $81, 27, 9, _, 1$?
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$3$. The common ratio in this geometric sequence is $\frac{1}{3}$, so multiply 9 by $\frac{1}{3}$ to find the missing term.
$3$. The common ratio in this geometric sequence is $\frac{1}{3}$, so multiply 9 by $\frac{1}{3}$ to find the missing term.
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What is the missing term in the sequence $100, 50, 25, _, \frac{25}{4}$ where each term is halved?
What is the missing term in the sequence $100, 50, 25, _, \frac{25}{4}$ where each term is halved?
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$\frac{25}{2}$. Each term is half the previous in this geometric sequence with ratio $\frac{1}{2}$, so divide 25 by 2.
$\frac{25}{2}$. Each term is half the previous in this geometric sequence with ratio $\frac{1}{2}$, so divide 25 by 2.
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What is the missing term in the arithmetic sequence $12, _, 4, 0, -4$?
What is the missing term in the arithmetic sequence $12, _, 4, 0, -4$?
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$8$. The common difference in this arithmetic sequence is -4, so subtract 4 from 12 to find the missing term.
$8$. The common difference in this arithmetic sequence is -4, so subtract 4 from 12 to find the missing term.
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What is the missing term in the arithmetic sequence $\frac{1}{2}, \frac{5}{2}, \frac{9}{2}, _, \frac{17}{2}$?
What is the missing term in the arithmetic sequence $\frac{1}{2}, \frac{5}{2}, \frac{9}{2}, _, \frac{17}{2}$?
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$\frac{13}{2}$. The common difference in this arithmetic sequence is 2, so add 2 to $\frac{9}{2}$ to find the missing term.
$\frac{13}{2}$. The common difference in this arithmetic sequence is 2, so add 2 to $\frac{9}{2}$ to find the missing term.
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What is the missing term in the sequence $9, 7, 10, 8, 11, _, 12$ that alternates $-2, +3$?
What is the missing term in the sequence $9, 7, 10, 8, 11, _, 12$ that alternates $-2, +3$?
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$9$. The pattern alternates subtracting 2 and adding 3, so subtract 2 from 11 to find the missing term.
$9$. The pattern alternates subtracting 2 and adding 3, so subtract 2 from 11 to find the missing term.
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What is the missing term in the sequence $2, 4, 8, 16, _, 64$ where each term doubles?
What is the missing term in the sequence $2, 4, 8, 16, _, 64$ where each term doubles?
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$32$. The common ratio in this geometric sequence is 2, so multiply 16 by 2 to find the missing term.
$32$. The common ratio in this geometric sequence is 2, so multiply 16 by 2 to find the missing term.
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What is the missing term in the Fibonacci-type sequence $1, 1, 2, 3, 5, _, 13$?
What is the missing term in the Fibonacci-type sequence $1, 1, 2, 3, 5, _, 13$?
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$8$. In this Fibonacci sequence, each term is the sum of the two preceding ones, so add 3 and 5.
$8$. In this Fibonacci sequence, each term is the sum of the two preceding ones, so add 3 and 5.
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What is the missing term in the sequence $1, 2, 4, 7, 11, _, 22$ where differences are $1,2,3,4,\dots$?
What is the missing term in the sequence $1, 2, 4, 7, 11, _, 22$ where differences are $1,2,3,4,\dots$?
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$16$. Differences increase by 1 starting from 1, so add 5 to 11 to find the missing term.
$16$. Differences increase by 1 starting from 1, so add 5 to 11 to find the missing term.
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What is the missing term in the triangular-number sequence $1, 3, 6, 10, _, 21$?
What is the missing term in the triangular-number sequence $1, 3, 6, 10, _, 21$?
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$15$. Triangular numbers are sums of the first n integers, so the fifth is $\frac{5 \times 6}{2}$.
$15$. Triangular numbers are sums of the first n integers, so the fifth is $\frac{5 \times 6}{2}$.
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What is the missing term in the sequence $6, 11, 21, 41, _, 161$ where each term is $2x-1$?
What is the missing term in the sequence $6, 11, 21, 41, _, 161$ where each term is $2x-1$?
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$81$. Each term is twice the previous minus 1, so apply the rule to 41 to find the missing term.
$81$. Each term is twice the previous minus 1, so apply the rule to 41 to find the missing term.
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What is the missing term in the sequence $1, 3, 7, 15, _, 63$ where each term is $2^n-1$?
What is the missing term in the sequence $1, 3, 7, 15, _, 63$ where each term is $2^n-1$?
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$31$. Each term follows the pattern $2^n - 1$ for consecutive integers n starting from 1, so use n=5.
$31$. Each term follows the pattern $2^n - 1$ for consecutive integers n starting from 1, so use n=5.
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What is the missing term in the cube-number sequence $1, 8, _, 64, 125$?
What is the missing term in the cube-number sequence $1, 8, _, 64, 125$?
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$27$. This sequence consists of cubes of consecutive integers, so the third term is $3^3$.
$27$. This sequence consists of cubes of consecutive integers, so the third term is $3^3$.
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What is the missing term in the square-number sequence $1, 4, 9, _, 25$?
What is the missing term in the square-number sequence $1, 4, 9, _, 25$?
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$16$. This sequence consists of squares of consecutive integers, so the fourth term is $4^2$.
$16$. This sequence consists of squares of consecutive integers, so the fourth term is $4^2$.
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What is the missing term in the geometric sequence $2, 6, 18, _, 162$?
What is the missing term in the geometric sequence $2, 6, 18, _, 162$?
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$54$. The common ratio in this geometric sequence is 3, so multiply 18 by 3 to find the missing term.
$54$. The common ratio in this geometric sequence is 3, so multiply 18 by 3 to find the missing term.
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What is the missing term in the arithmetic sequence $5, 9, 13, _, 21$?
What is the missing term in the arithmetic sequence $5, 9, 13, _, 21$?
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$17$. The common difference in this arithmetic sequence is 4, so add 4 to 13 to find the missing term.
$17$. The common difference in this arithmetic sequence is 4, so add 4 to 13 to find the missing term.
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What is the missing term in the geometric sequence $\frac{3}{2}, \frac{3}{4}, _, \frac{3}{16}$?
What is the missing term in the geometric sequence $\frac{3}{2}, \frac{3}{4}, _, \frac{3}{16}$?
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$\frac{3}{8}$. The common ratio in this geometric sequence is $\frac{1}{2}$, so multiply $\frac{3}{4}$ by $\frac{1}{2}$ to find the missing term.
$\frac{3}{8}$. The common ratio in this geometric sequence is $\frac{1}{2}$, so multiply $\frac{3}{4}$ by $\frac{1}{2}$ to find the missing term.
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What is the missing term in the arithmetic sequence $-3, 1, 5, _, 13$?
What is the missing term in the arithmetic sequence $-3, 1, 5, _, 13$?
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$9$. The common difference in this arithmetic sequence is 4, so add 4 to 5 to find the missing term.
$9$. The common difference in this arithmetic sequence is 4, so add 4 to 5 to find the missing term.
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