Find the Missing Terms: Solving 2+4, 3+7, 4+10, 5+13 Sequence Pattern

Q: Why do I look at columns separately instead of the whole expression?

Each column follows its own arithmetic sequence! The left numbers (2, 3, 4, 5) increase by 1, while the right numbers (4, 7, 10, 13) increase by 3. Finding patterns within columns is much clearer.

Q: How do I know which direction to work backwards?

Since you're looking for the first term, subtract the pattern difference from the known first values: $ 2-1=1 $ and $ 4-3=1 $.

Arithmetic Sequences with Two-Column Patterns

The sequence below is structured according to a term-to-term rule.

What is the first element?

$\text{?}+\text{?}$

$2+4$

$3+7$

$4+10$

$5+13$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the first exercise

00:03 We'll observe the change between elements on the left side

00:11 We'll derive from the pattern the left side of the first exercise

00:20 Now we'll use the same method for the right side of the exercise

00:24 We'll observe the change between elements on the right side

00:29 We'll derive from the pattern the right side of the first exercise

00:39 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The sequence below is structured according to a term-to-term rule.

What is the first element?

$\text{?}+\text{?}$

$2+4$

$3+7$

$4+10$

$5+13$

Step-by-step solution

We start with the right column in the exercises.

Between each number there is a jump of +3: $4+3=7$

$7+3=10$

Etcetera.

Now we move to the left column of the exercises.

Between each number there is a jump of +1:

$2+1=3$

$3+1=4$

Now we can figure out which exercise is missing:

The left digit will be: $2-1=1$

The right digit will be: $4-3=1$

And the missing exercise is: $1+1$

Final Answer

$1+1$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Identify consistent differences in both columns separately
Technique: Left column increases by 1, right column by 3
Check: Missing term follows pattern: $1+1$ fits sequence perfectly ✓

Common Mistakes

Avoid these frequent errors

Looking for pattern across rows instead of within columns
Don't try to find relationships between 2 and 4, or 3 and 7 = confusing wrong patterns! This misses the actual structure. Always examine each column separately to find the consistent increment pattern.

Practice Quiz

Test your knowledge with interactive questions

Is there a term-to-term rule for the sequence below?

18 , 22 , 26 , 30

FAQ

Everything you need to know about this question

Why do I look at columns separately instead of the whole expression?

Each column follows its own arithmetic sequence! The left numbers (2, 3, 4, 5) increase by 1, while the right numbers (4, 7, 10, 13) increase by 3. Finding patterns within columns is much clearer.

How do I know which direction to work backwards?

Since you're looking for the first term, subtract the pattern difference from the known first values: $2-1=1$ and $4-3=1$ .

What if the differences aren't the same in a column?

Then it's not an arithmetic sequence! Check your work by calculating differences again. In true arithmetic sequences, the common difference stays constant throughout.

Can I check my answer another way?

Yes! Verify that your missing term creates the right pattern: $1+1$ , then $2+4$ - both columns should increase by their expected amounts.

Do both columns always have to start with the same number?

Not at all! Each column follows its own sequence independently. It's just a coincidence that both start with 1 in this problem. Focus on each column's individual pattern.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Series questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime