ISEE Upper Level Quantitative Reasoning Flashcards: Missing Terms In Sequences

What this deck covers

This deck focuses on Missing Terms In Sequences, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Upper Level Quantitative Reasoning.

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 missing term in the arithmetic sequence $-3, 1, 5, _, 13$?

Answer: $9$. The common difference in this arithmetic sequence is 4, so add 4 to 5 to find the missing term.

Flashcard 2: What is the missing term in the arithmetic sequence $12, _, 4, 0, -4$?

Answer: $8$. The common difference in this arithmetic sequence is -4, so subtract 4 from 12 to find the missing term.

Flashcard 3: What is the missing term in the geometric sequence $\frac{3}{2}, \frac{3}{4}, _, \frac{3}{16}$?

Answer: $\frac{3}{8}$. 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.

Flashcard 4: What is the missing term in the Fibonacci-type sequence $1, 1, 2, 3, 5, _, 13$?

Answer: $8$. In this Fibonacci sequence, each term is the sum of the two preceding ones, so add 3 and 5.

Flashcard 5: What is the missing term in the arithmetic sequence $\frac{1}{2}, \frac{5}{2}, \frac{9}{2}, _, \frac{17}{2}$?

Answer: $\frac{13}{2}$. The common difference in this arithmetic sequence is 2, so add 2 to $\frac{9}{2}$ to find the missing term.

Flashcard 6: What is the missing term in the square-number sequence $1, 4, 9, _, 25$?

Answer: $16$. This sequence consists of squares of consecutive integers, so the fourth term is $4^2$.

Flashcard 7: What is the missing term in the sequence $3, 7, 13, 21, _, 43$ where each term is $n^2+n+1$?

Answer: $31$. Each term follows the pattern $n^2 + n + 1$ for consecutive integers n starting from 1, so use n=5.

Flashcard 8: What is the missing term in the arithmetic sequence $5, 9, 13, _, 21$?

Answer: $17$. The common difference in this arithmetic sequence is 4, so add 4 to 13 to find the missing term.

Flashcard 9: What is the missing term in the sequence $2, 3, 5, 8, 12, _, 23$ where differences increase by $1$?

Answer: $17$. Differences increase by 1 starting from 1, so add 5 to 12 to find the missing term.

Flashcard 10: What is the missing term in the sequence $100, 50, 25, _, \frac{25}{4}$ where each term is halved?

Answer: $\frac{25}{2}$. Each term is half the previous in this geometric sequence with ratio $\frac{1}{2}$, so divide 25 by 2.

Flashcard 11: What is the missing term in the sequence $2, 4, 8, 16, _, 64$ where each term doubles?

Answer: $32$. The common ratio in this geometric sequence is 2, so multiply 16 by 2 to find the missing term.

Flashcard 12: What is the missing term in the geometric sequence $81, 27, 9, _, 1$?

Answer: $3$. The common ratio in this geometric sequence is $\frac{1}{3}$, so multiply 9 by $\frac{1}{3}$ to find the missing term.

Flashcard 13: What is the missing term in the sequence $1, 2, 4, 7, 11, _, 22$ where differences are $1,2,3,4,\dots$?

Answer: $16$. Differences increase by 1 starting from 1, so add 5 to 11 to find the missing term.

Flashcard 14: What is the missing term in the cube-number sequence $1, 8, _, 64, 125$?

Answer: $27$. This sequence consists of cubes of consecutive integers, so the third term is $3^3$.

Flashcard 15: What is the missing term in the geometric sequence $2, 6, 18, _, 162$?

Answer: $54$. The common ratio in this geometric sequence is 3, so multiply 18 by 3 to find the missing term.

Flashcard 16: What is the missing term in the triangular-number sequence $1, 3, 6, 10, _, 21$?

Answer: $15$. Triangular numbers are sums of the first n integers, so the fifth is $\frac{5 \times 6}{2}$.

Flashcard 17: What is the missing term in the sequence $9, 7, 10, 8, 11, _, 12$ that alternates $-2, +3$?

Answer: $9$. The pattern alternates subtracting 2 and adding 3, so subtract 2 from 11 to find the missing term.

Flashcard 18: What is the missing term in the sequence $6, 11, 21, 41, _, 161$ where each term is $2x-1$?

Answer: $81$. Each term is twice the previous minus 1, so apply the rule to 41 to find the missing term.

Flashcard 19: What is the missing term in the sequence $2, 5, 10, 17, _, 37$ where each term is $n^2+1$?

Answer: $26$. Each term follows the pattern $n^2 + 1$ for consecutive integers n starting from 1, so use n=5.

Flashcard 20: What is the missing term in the sequence $1, 2, 6, 24, _, 720$?

Answer: $120$. This sequence follows the factorial pattern $n!$, so the fifth term is $5!$.

Flashcard 21: What is the missing term in the sequence $1, 3, 7, 15, _, 63$ where each term is $2^n-1$?

Answer: $31$. Each term follows the pattern $2^n - 1$ for consecutive integers n starting from 1, so use n=5.