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

Q: What does n represent in the formula?

The variable n represents the position of the term in the sequence. For the third term, n = 3, for the fifth term, n = 5, and so on.

Q: How do I know if I calculated correctly?

Calculate a few terms to check the pattern. For $ n^2 + 1 $: first term (n=1) gives 2, second term (n=2) gives 5, third term (n=3) gives 10.

Sequence Terms with Substitution Method

For the series $n^2+1$

What is the third element?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the third term in the sequence

00:04 Substitute the term number (N) in the formula and solve

00:22 Calculate the power

00:33 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

For the series $n^2+1$

What is the third element?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Use the formula $n^2 + 1$ to find the first element when $n = 1$ .
Step 2: Use the formula $n^2 + 1$ to find the second element when $n = 2$ .
Step 3: Use the formula $n^2 + 1$ to find the third element when $n = 3$ .

Let's work through each step:

Step 1: For the first element, substitute $n = 1$ into the formula:
$1^2 + 1 = 1 + 1 = 2$ .

Step 2: For the second element, substitute $n = 2$ into the formula:
$2^2 + 1 = 4 + 1 = 5$ .

Step 3: For the third element, substitute $n = 3$ into the formula:
$3^2 + 1 = 9 + 1 = 10$ .

Therefore, the third element of the series is 10.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula Rule: Substitute position value n into the given formula
Technique: For third term, calculate $3^2 + 1 = 9 + 1 = 10$
Check: Verify by computing first few terms: 2, 5, 10 follows pattern ✓

Common Mistakes

Avoid these frequent errors

Using the term number as the answer directly
Don't assume the third term equals 3! The formula $n^2 + 1$ transforms the position number. When n=3, you get $3^2 + 1 = 10$ , not 3. Always substitute the position number into the complete formula.

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 n represent in the formula?

The variable n represents the position of the term in the sequence. For the third term, n = 3, for the fifth term, n = 5, and so on.

Do I always start with n = 1 for the first term?

Yes! Unless stated otherwise, sequences typically start with n = 1 for the first term, n = 2 for the second term, etc.

How do I know if I calculated correctly?

Calculate a few terms to check the pattern. For $n^2 + 1$ : first term (n=1) gives 2, second term (n=2) gives 5, third term (n=3) gives 10.

What if the formula has multiple variables?

This formula only has n as the variable. Simply substitute the position number for n and follow the order of operations (exponents first, then addition).

Can sequence terms be negative?

Yes! Depending on the formula and position number, sequence terms can be negative, positive, or zero. Always compute exactly what the formula gives you.

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