Find the Fifth Term in the n²-1 Sequence: Step-by-Step Solution

Q: What does 'fifth term' actually mean in a sequence?

The fifth term means the value when n = 5. You substitute 5 into the formula $ n^2 - 1 $, not that the answer is 5!

Q: Do I always square first, then subtract?

Yes! Follow the order of operations (PEMDAS). Calculate $ n^2 $ first, then subtract 1. So $ 5^2 - 1 = 25 - 1 = 24 $.

Q: How can I check if 24 is really the fifth term?

Substitute back: when n = 5, does $ 5^2 - 1 = 24 $? Yes! $ 25 - 1 = 24 $ ✓

Q: Why isn't the answer 25?

Because we need $ n^2 - 1 $, not just $ n^2 $! Don't forget the subtract 1 part. $ 5^2 = 25 $, but $ 5^2 - 1 = 24 $.

Sequence Formula with Direct Substitution

$n^2-1$

What is the fifth term in the above sequence?

❤️ 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 Find the 5th element

00:03 Let's substitute the position of the matching element in the formula and solve

00:16 Always solve exponents first

00:23 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

$n^2-1$

What is the fifth term in the above sequence?

Step-by-step solution

To solve this problem, we'll directly calculate the fifth term of the sequence defined by $n^2 - 1$ :

Step 1: Use the given formula for the sequence, $n^2 - 1$ .
Step 2: Substitute $n = 5$ , as we need the fifth term.
Step 3: Calculate $5^2 - 1$ .

Now, perform these calculations:
Substitute $n = 5$ :
$n^2 - 1 = 5^2 - 1$ .
Calculate $5^2 = 25$ .
Then subtract 1: $25 - 1 = 24$ .

Therefore, the fifth term in the sequence is $24$ , which matches choice 2 from the provided options.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Use the given expression $n^2 - 1$ to find any term
Technique: Substitute n = 5 directly: $5^2 - 1 = 25 - 1 = 24$
Check: Verify by calculating step by step: square first, then subtract ✓

Common Mistakes

Avoid these frequent errors

Confusing term position with term value
Don't think the fifth term equals 5 because it's in position 5 = wrong answer! The position number goes INTO the formula, not equals the result. Always substitute the position number (5) into the formula $n^2 - 1$ to get the term value.

Practice Quiz

Test your knowledge with interactive questions

12 ☐ 10 ☐ 8 7 6 5 4 3 2 1

Which numbers are missing from the sequence so that the sequence has a term-to-term rule?

FAQ

Everything you need to know about this question

What does 'fifth term' actually mean in a sequence?

The fifth term means the value when n = 5. You substitute 5 into the formula $n^2 - 1$ , not that the answer is 5!

Do I always square first, then subtract?

Yes! Follow the order of operations (PEMDAS). Calculate $n^2$ first, then subtract 1. So $5^2 - 1 = 25 - 1 = 24$ .

How can I check if 24 is really the fifth term?

Substitute back: when n = 5, does $5^2 - 1 = 24$ ? Yes! $25 - 1 = 24$ ✓

What would the first few terms of this sequence be?

Let's see:

n = 1: $1^2 - 1 = 0$
n = 2: $2^2 - 1 = 3$
n = 3: $3^2 - 1 = 8$
n = 4: $4^2 - 1 = 15$

So the sequence is: 0, 3, 8, 15, 24, ...

Why isn't the answer 25?

Because we need $n^2 - 1$ , not just $n^2$ ! Don't forget the subtract 1 part. $5^2 = 25$ , but $5^2 - 1 = 24$ .

🌟 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