Predicting Later Terms - SSAT Middle Level: Quantitative
Card 1 of 19
What is the $8$th term of the pattern $1, 3, 6, 10, 15, \dots$?
What is the $8$th term of the pattern $1, 3, 6, 10, 15, \dots$?
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$36$. The sequence is triangular numbers, where the $n$th term is $\frac{n(n+1)}{2}$.
$36$. The sequence is triangular numbers, where the $n$th term is $\frac{n(n+1)}{2}$.
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What is the next term in the arithmetic pattern $7, 11, 15, 19, \dots$?
What is the next term in the arithmetic pattern $7, 11, 15, 19, \dots$?
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$23$. The sequence is arithmetic with a common difference of $4$, so add $4$ to the last term to find the next.
$23$. The sequence is arithmetic with a common difference of $4$, so add $4$ to the last term to find the next.
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What is the next term in the pattern $100, 50, 25, 12.5, \dots$?
What is the next term in the pattern $100, 50, 25, 12.5, \dots$?
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$6.25$. The geometric sequence has a common ratio of $\frac{1}{2}$, so multiply the last term by $\frac{1}{2}$.
$6.25$. The geometric sequence has a common ratio of $\frac{1}{2}$, so multiply the last term by $\frac{1}{2}$.
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What is the next term in the pattern $2, 6, 12, 20, 30, \dots$?
What is the next term in the pattern $2, 6, 12, 20, 30, \dots$?
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$42$. The sequence follows $n(n+1)$ for consecutive integers $n$ starting from $1$, so use $n=6$.
$42$. The sequence follows $n(n+1)$ for consecutive integers $n$ starting from $1$, so use $n=6$.
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What is the next term in the pattern $3, 6, 10, 15, 21, \dots$?
What is the next term in the pattern $3, 6, 10, 15, 21, \dots$?
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$28$. The sequence is triangular numbers where differences increase by $1$ starting from $3$, so add $7$ to the last term.
$28$. The sequence is triangular numbers where differences increase by $1$ starting from $3$, so add $7$ to the last term.
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What is the next term in the alternating pattern $10, 7, 14, 11, 18, 15, \dots$?
What is the next term in the alternating pattern $10, 7, 14, 11, 18, 15, \dots$?
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$22$. The pattern alternates subtracting $3$ and adding $7$, so add $7$ after the last subtraction.
$22$. The pattern alternates subtracting $3$ and adding $7$, so add $7$ after the last subtraction.
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What is the next term in the Fibonacci-type pattern $1, 1, 2, 3, 5, 8, \dots$?
What is the next term in the Fibonacci-type pattern $1, 1, 2, 3, 5, 8, \dots$?
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$13$. The sequence follows the Fibonacci rule where each term is the sum of the two preceding ones.
$13$. The sequence follows the Fibonacci rule where each term is the sum of the two preceding ones.
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What is the $6$th term of the cube-number pattern $1, 8, 27, 64, \dots$?
What is the $6$th term of the cube-number pattern $1, 8, 27, 64, \dots$?
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$216$. The sequence is cubes of consecutive integers starting from $1$, so the $n$th term is $n^3$.
$216$. The sequence is cubes of consecutive integers starting from $1$, so the $n$th term is $n^3$.
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What is the next term in the pattern $1, 8, 27, 64, \dots$?
What is the next term in the pattern $1, 8, 27, 64, \dots$?
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$125$. The sequence consists of cubes of consecutive integers, so cube the next integer after $4$.
$125$. The sequence consists of cubes of consecutive integers, so cube the next integer after $4$.
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What is the next term in the pattern $\frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \dots$?
What is the next term in the pattern $\frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \dots$?
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$\frac{6}{7}$. Both numerator and denominator increase by $1$ each time, starting from $\frac{2}{3}$.
$\frac{6}{7}$. Both numerator and denominator increase by $1$ each time, starting from $\frac{2}{3}$.
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What is the next term in the pattern $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \dots$?
What is the next term in the pattern $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \dots$?
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$\frac{1}{32}$. The geometric sequence has a common ratio of $\frac{1}{2}$, so multiply the last term by $\frac{1}{2}$.
$\frac{1}{32}$. The geometric sequence has a common ratio of $\frac{1}{2}$, so multiply the last term by $\frac{1}{2}$.
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What is the $10$th term of the arithmetic sequence $3, 8, 13, 18, \dots$?
What is the $10$th term of the arithmetic sequence $3, 8, 13, 18, \dots$?
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$48$. The arithmetic sequence has first term $3$ and common difference $5$, so the $n$th term is $3 + (n-1) \times 5$.
$48$. The arithmetic sequence has first term $3$ and common difference $5$, so the $n$th term is $3 + (n-1) \times 5$.
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What is the next term in the geometric pattern $2, 6, 18, 54, \dots$?
What is the next term in the geometric pattern $2, 6, 18, 54, \dots$?
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$162$. The geometric sequence has a common ratio of $3$, so multiply the last term by $3$ to find the next.
$162$. The geometric sequence has a common ratio of $3$, so multiply the last term by $3$ to find the next.
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What is the $7$th term of the geometric sequence $5, 10, 20, 40, \dots$?
What is the $7$th term of the geometric sequence $5, 10, 20, 40, \dots$?
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$320$. The geometric sequence has first term $5$ and common ratio $2$, so the $n$th term is $5 \times 2^{n-1}$.
$320$. The geometric sequence has first term $5$ and common ratio $2$, so the $n$th term is $5 \times 2^{n-1}$.
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What is the next term in the pattern $1, 4, 9, 16, 25, \dots$?
What is the next term in the pattern $1, 4, 9, 16, 25, \dots$?
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$36$. The sequence consists of squares of consecutive integers, so square the next integer after $5$.
$36$. The sequence consists of squares of consecutive integers, so square the next integer after $5$.
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What is the $12$th term of the square-number pattern $1, 4, 9, 16, \dots$?
What is the $12$th term of the square-number pattern $1, 4, 9, 16, \dots$?
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$144$. The sequence is squares of consecutive integers starting from $1$, so the $n$th term is $n^2$.
$144$. The sequence is squares of consecutive integers starting from $1$, so the $n$th term is $n^2$.
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What is the next term in the pattern $\frac{1}{2}, 1, \frac{3}{2}, 2, \frac{5}{2}, \dots$?
What is the next term in the pattern $\frac{1}{2}, 1, \frac{3}{2}, 2, \frac{5}{2}, \dots$?
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$3$. The arithmetic sequence increases by $\frac{1}{2}$ each time, so add $\frac{1}{2}$ to the last term.
$3$. The arithmetic sequence increases by $\frac{1}{2}$ each time, so add $\frac{1}{2}$ to the last term.
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What is the next term in the pattern $4, 9, 19, 39, 79, \dots$?
What is the next term in the pattern $4, 9, 19, 39, 79, \dots$?
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$159$. Each term is obtained by doubling the previous and adding $1$.
$159$. Each term is obtained by doubling the previous and adding $1$.
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What is the next term in the pattern $2, 3, 5, 8, 12, \dots$?
What is the next term in the pattern $2, 3, 5, 8, 12, \dots$?
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$17$. Differences increase by $1$ starting from $+1$, so add $5$ to the last term.
$17$. Differences increase by $1$ starting from $+1$, so add $5$ to the last term.
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