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?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 We are going to find the fifth element.

00:08 Let's substitute the position of the element into the formula. Then, we'll solve step by step.

00:21 Remember, always solve the exponents first. Good job!

00:28 And there you have it, the solution to our 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

Look at the following set of numbers and determine if there is any property, if so, what is it?

$$ 94,96,98,100,102,104 $$

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 $5^2 - 1 = 24$ .

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