Sequences and patterns — ISEE Upper practice questions

Sequences and patterns on the ISEE Upper Quantitative Reasoning section covers finding a later term in a growing list, recognizing a shared operation between consecutive terms, and locating a position in a repeating cycle. A student has to apply a constant change such as two extra seats in each following row, match another sequence that uses that same rule, and map a far later day onto a six-day weather order that repeats indefinitely. Questions are short word problems whose choices are usually a single number, a rival sequence, or a weather label. Common traps are off-by-one row or day counts and confusing one term with a total.

Section: Quantitative Reasoning 37 questions on the paper
69 practice questions in the app

Sample questions

Question 1

In an auditorium, the first row has 12 seats. Each row after the first has 2 more seats than the row before it. How many seats are in the 10th row?

Show answer

Answer: C — 30

From row 1 to row 10, there are 9 increases. Each increase adds 2 seats, so the 10th row has $12+9\times2=30$ seats.

Question 2

A sequence begins $2,\ 8,\ 32,\ 128,\ \dots$ , with the same operation used to obtain each term from the preceding term. Which sequence uses that same operation between consecutive terms?

A $128,\ 32,\ 8,\ 2,\ \dots$
B $3,\ 7,\ 11,\ 15,\ \dots$
C $1,\ 4,\ 16,\ 64,\ \dots$
D $2,\ 6,\ 18,\ 54,\ \dots$

Show answer

Answer: C — $1,\ 4,\ 16,\ 64,\ \dots$

Each term in the given sequence is found by multiplying the previous term by 4 ( $2\times4=8$ , $8\times4=32$ , $32\times4=128$ ). Only $1,\ 4,\ 16,\ 64,\dots$ is built by repeatedly multiplying by 4.

Question 3

In a fictional town, the weather follows a strict 6-day repeating pattern, starting on Day 1: sunny, sunny, cloudy, rainy, cloudy, windy, and then the same six-day order repeats indefinitely. What is the weather on Day 50?

Acloudy
Bsunny
Cwindy
Drainy

Show answer

Answer: B — sunny

Dividing 50 by the cycle length 6 gives a remainder of 2 (since $48=6\times8$ ), so Day 50 has the same weather as Day 2, which is sunny.

Practice 69 Sequences and patterns questions in the app

Sequences and patterns — ISEE Upper practice questions

Sample questions

More ISEE Upper topics

Quantitative Reasoning