SSAT Upper Level Quantitative Flashcards: Numerical Sequence Patterns

What this deck covers

This deck focuses on Numerical Sequence Patterns, giving you a quick way to review the definitions, rules, and examples that matter most for SSAT Upper Level Quantitative.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the common difference in the arithmetic sequence $-3, 2, 7, 12, \dots$?

Answer: $5$. The common difference is calculated by subtracting consecutive terms, yielding a constant $5$.

Flashcard 2: What is the next term in the geometric sequence $3, 6, 12, 24, \dots$?

Answer: $48$. The sequence is geometric with a common ratio of $2$, so the next term is obtained by multiplying $24$ by $2$.

Flashcard 3: What is the next term in the sequence $10, 7, 14, 11, 22, 19, \dots$?

Answer: $38$. The pattern alternates subtracting $3$ and multiplying by $2$, applying multiplication by $2$ to $19$.

Flashcard 4: What is the common ratio in the geometric sequence $81, 27, 9, 3, \dots$?

Answer: $\frac{1}{3}$. The common ratio is determined by dividing consecutive terms, resulting in $\frac{1}{3}$ consistently.

Flashcard 5: What is the next term in the sequence $3, 7, 15, 31, 63, \dots$?

Answer: $127$. Each term is one less than a power of $2$, specifically $2^{n+1} - 1$, with the next for $n=6$.

Flashcard 6: What is the next term in the sequence of perfect squares $1, 4, 9, 16, 25, \dots$?

Answer: $36$. The sequence consists of squares of consecutive integers, with the next being $6^2$.

Flashcard 7: What is the next term in the sequence $-1, 2, -4, 8, -16, \dots$?

Answer: $32$. The geometric sequence has a common ratio of $-2$, alternating signs while doubling in magnitude.

Flashcard 8: What is the next term in the sequence $100, 50, 25, 12.5, \dots$?

Answer: $6.25$. The geometric sequence has a common ratio of $\frac{1}{2}$, halving each term.

Flashcard 9: What is the next term in the sequence $1, 3, 6, 10, 15, 21, \dots$?

Answer: $28$. This is the sequence of triangular numbers, where each adds the next integer, so $21 + 7$.

Flashcard 10: What is the next term in the sequence of triangular numbers $1, 3, 6, 10, 15, \dots$?

Answer: $21$. Triangular numbers sum the first $n$ natural numbers, so the next adds $6$ to $15$.

Flashcard 11: What is the next term in the sequence with increasing differences $1, 2, 4, 7, 11, \dots$?

Answer: $16$. Differences increase by $1$ each time starting from $1$, so add $5$ to $11$.

Flashcard 12: What is the next term in the sequence $4, 9, 16, 25, 36, \dots$?

Answer: $49$. The sequence is squares of integers starting from $2$, with the next being $7^2$.

Flashcard 13: What is the next term in the Fibonacci-type sequence $2, 3, 5, 8, 13, \dots$?

Answer: $21$. Each term is the sum of the two preceding ones, following a Fibonacci-like pattern starting from $2$ and $3$.

Flashcard 14: What is the next term in the sequence $2, 5, 10, 17, 26, \dots$?

Answer: $37$. Differences are odd numbers starting from $3$ and increasing by $2$, so add $11$ to $26$.

Flashcard 15: What is the next term in the arithmetic sequence $7, 12, 17, 22, \dots$?

Answer: $27$. The sequence is arithmetic with a common difference of $5$, so the next term is found by adding $5$ to $22$.

Flashcard 16: What is the $n$th-term formula for a geometric sequence with first term $a_1$ and ratio $r$?

Answer: $a_n = a_1 r^{n-1}$. This formula computes the $n$th term by multiplying the first term $a_1$ by the common ratio $r$ raised to the power of $n-1$.

Flashcard 17: What is the next term in the alternating sequence $5, -5, 5, -5, \dots$?

Answer: $5$. The sequence alternates between positive and negative $5$, so after $-5$ it returns to positive.

Flashcard 18: What is the next term in the sequence $2, 3, 5, 9, 17, \dots$?

Answer: $33$. Each term is twice the previous minus $1$, applying the rule to $17$.

Flashcard 19: What is the next term in the sequence of perfect cubes $1, 8, 27, 64, \dots$?

Answer: $125$. The sequence comprises cubes of consecutive integers, with the next being $5^3$.

Flashcard 20: What is the next term in the sequence $2, 4, 7, 11, 16, \dots$?

Answer: $22$. Differences increase by $1$ starting from $2$, so add $6$ to $16$.

Flashcard 21: What is the explicit formula for the $n$th triangular number $T_n$?

Answer: $T_n = \frac{n(n+1)}{2}$. The formula sums the first $n$ positive integers to yield the $n$th triangular number.

Flashcard 22: What is the $n$th-term formula for an arithmetic sequence with first term $a_1$ and common difference $d$?

Answer: $a_n = a_1 + (n-1)d$. This formula derives the $n$th term by starting from $a_1$ and adding the common difference $d$ for each subsequent term up to $n-1$.

Flashcard 23: What is the next term in the sequence $1, 4, 2, 8, 4, 16, \dots$?

Answer: $8$. The pattern alternates between multiplying by $4$ and dividing by $2$, so divide $16$ by $2$.