Square Sequence Formula: Identifying the Pattern Expression

Q: How do I know which formula is correct when multiple seem close?

Test each formula with at least 2-3 position values from the sequence. The correct formula will match every single term you calculate.

Q: Why is the answer 2n-1 and not 2n+1?

Because $ 2n-1 $ gives us the odd numbers starting from 1. When n=1: 2(1)-1=1. When n=2: 2(2)-1=3. The formula $ 2n+1 $ would start at 3!

Q: Is there a pattern to recognize odd number sequences?

Yes! Odd number sequences like 1, 3, 5, 7... always follow $ 2n-1 $. Each term increases by 2, and they're all odd numbers.

Sequence Patterns with Odd Number Formula

Which formula corresponds to the number of squares in the above sequence?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the sequence formula

00:03 Let's observe the number of squares in each term

00:21 Let's substitute the first term in equations and see if it fits

00:35 We can see that this formula doesn't fit

00:40 Let's continue with this method until we find the correct formula

00:51 This formula doesn't fit either

00:54 This formula fits the first term

00:59 And this formula also fits the first term

01:02 Let's check which formula also fits the second term

01:09 This formula doesn't fit the second term, so it's not the formula

01:23 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

Which formula corresponds to the number of squares in the above sequence?

Final Answer

$2n-1$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Count squares in each figure to identify the sequence
Testing Formula: Substitute position values: n=1 gives 2(1)-1 = 1 square
Verification: Check multiple terms: position 2 gives 2(2)-1 = 3 squares ✓

Common Mistakes

Avoid these frequent errors

Confusing position number with actual count
Don't assume the formula is just n because the first figure has 1 square = missing the pattern! This ignores how the sequence actually grows. Always count the squares in each position and test which formula matches all terms.

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

How do I know which formula is correct when multiple seem close?

Test each formula with at least 2-3 position values from the sequence. The correct formula will match every single term you calculate.

What if I can't see the pattern clearly in the diagram?

Count the squares systematically! Go position by position: 1st figure has 1 square, 2nd has 3 squares, 3rd has 5 squares. Write down the sequence: 1, 3, 5...

Why is the answer 2n-1 and not 2n+1?

Because $2n-1$ gives us the odd numbers starting from 1. When n=1: 2(1)-1=1. When n=2: 2(2)-1=3. The formula $2n+1$ would start at 3!

Is there a pattern to recognize odd number sequences?

Yes! Odd number sequences like 1, 3, 5, 7... always follow $2n-1$ . Each term increases by 2, and they're all odd numbers.

How can I double-check my answer?

Pick any position and substitute into your chosen formula. For example, if the 4th figure should have 7 squares, check: $2(4)-1 = 8-1 = 7$ ✓

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