01 / 20
?

Missing Sequence Terms
Find the Pattern

Learn how to spot the rule in a list of numbers and fill in the missing term.

ISEE Lower Level: Quantitative Reasoning

What Is a Sequence?

A sequence is an ordered list of numbers that follows a rule. Each number in the list is called a term.

2 4 6 8 1st term 2nd term 3rd term 4th term ...

A Missing Term

Sometimes a term is hidden, shown as a blank or a ?. Your job is to find the rule, then use it to fill the blank.

5 10 ? 20

Why This Matters

Everyday Patterns
Counting by 2s, 5s, or 10s, like skip-counting money or pages.
Test Smarts
ISEE questions reward spotting patterns quickly and checking your answer.
Math Power
Finding rules builds the thinking you need for algebra later on.

Two Common Patterns

Add or Subtract
The same number is added or taken away each step. Example: \( 3, 6, 9, 12 \) adds 3.
Multiply or Divide
Each term is multiplied or divided by the same number. Example: \( 2, 4, 8, 16 \) multiplies by 2.

Find the Difference

For an "add" pattern, look at the gap between two terms next to each other. That gap is the rule.

7 11 15 19
\(+4\)
\(+4\)
\(+4\)
The rule is: add 4

Going Up vs. Going Down

Look at whether the numbers get bigger or smaller as you move right. This tells you to add or subtract.

Getting Bigger ↑
You are adding or multiplying. Example: \( 4, 8, 12, 16 \).
Getting Smaller ↓
You are subtracting or dividing. Example: \( 20, 16, 12, 8 \).

How to Find a Missing Term

1
Look at the numbers and decide if they go up or down.
2
Find the rule by checking the gap between two terms you can see.
3
Check the rule works between more than one pair of terms.
4
Apply the rule to fill in the blank, then read it back to be sure.

Example 1: Add Pattern

Find the missing term: \( 3, \ 6, \ 9, \ ?, \ 15 \)

3 6 9 ? 15
\(+3\)
\(+3\)

Example 2: Subtract Pattern

Find the missing term: \( 30, \ 25, \ ?, \ 15, \ 10 \)

30 25 ? 15 10
\({-}5\)
\({-}5\)

Example 3: Multiply Pattern

Find the missing term: \( 1, \ 2, \ 4, \ ?, \ 16 \)

1 2 4 ? 16
\(\times 2\)
\(\times 2\)

Common Mistakes

✕ Wrong Direction
Adding when the numbers are actually going down. Always check up or down first.
✕ Checking Only Once
Test the rule on more than one pair so you are sure it is the real pattern.
✕ Mixing Rules
Using add for one gap and multiply for the next. The rule stays the same all the way.

Pattern Summary

Direction Example
AddGoes up\( 2, 4, 6, 8 \)
SubtractGoes down\( 20, 15, 10, 5 \)
MultiplyUp fast\( 3, 6, 12, 24 \)
DivideDown fast\( 80, 40, 20, 10 \)

Question 1 of 5

What is the missing term? \( 4, \ 8, \ ?, \ 16, \ 20 \)

Question 2 of 5

What is the missing term? \( 25, \ 20, \ 15, \ ?, \ 5 \)

Question 3 of 5

What is the missing term? \( 3, \ 6, \ 12, \ ?, \ 48 \)

Question 4 of 5

What is the missing term? \( 100, \ ?, \ 80, \ 70, \ 60 \)

Question 5 of 5

What is the missing term? \( 7, \ 14, \ 21, \ 28, \ ? \)

Quick Strategy

1
Up or down? Check the direction of the numbers.
2
Find the gap between two terms to get the rule.
3
Apply and check the rule before choosing your answer.

You Found the Pattern!

Remember: spot the rule, apply it, then check. You can solve any missing-term sequence.