Evaluate the Sequence: Finding the First Term in 6n² - 1

Q: What if the problem asked for the 3rd term instead?

Simply substitute n = 3 into the formula! For $ 6n^2 - 1 $, you'd get $ 6(3)^2 - 1 = 6(9) - 1 = 53 $.

Q: Can sequence formulas have negative terms?

Absolutely! Depending on the formula and position n, terms can be positive, negative, or zero. Always calculate exactly what the formula gives you.

Q: Do I need to simplify 6(1)² before subtracting 1?

Yes! Follow the order of operations: first calculate the exponent (1² = 1), then multiply (6 × 1 = 6), then subtract (6 - 1 = 5).

Sequence Evaluation with Quadratic Formulas

A sequence has the rule $6n^2-1$ .

What is the first term?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the first term

00:03 We'll substitute the appropriate term's position in the formula and solve

00:17 Always solve exponents first

00:23 Always solve multiplication and division before addition and subtraction

00:28 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

A sequence has the rule $6n^2-1$ .

What is the first term?

Step-by-step solution

To solve this problem, we'll calculate the first term of the sequence defined by the rule $6n^2 - 1$ :

Step 1: Identify the position for the first term. By convention, this position is $n = 1$ .
Step 2: Substitute $n = 1$ into the formula $6n^2 - 1$ :

Substitution and calculation:

For $n = 1$ , the expression becomes $6(1)^2 - 1$ .

Calculate $6(1)^2$ : $6 \times 1 = 6$ .

Subtract 1 from 6: $6 - 1 = 5$ .

Therefore, the first term of the sequence is $\boxed{5}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: First term occurs when n = 1 in any sequence formula
Technique: Substitute n = 1: $6(1)^2 - 1 = 6 - 1 = 5$
Check: Verify by calculating second term: $6(2)^2 - 1 = 23$ ✓

Common Mistakes

Avoid these frequent errors

Starting with n = 0 instead of n = 1
Don't use n = 0 to find the first term = gives 6(0)² - 1 = -1! This assumes sequences start at position zero, but by convention the first term corresponds to n = 1. Always substitute n = 1 for the first term of any sequence.

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

Why do we use n = 1 for the first term instead of n = 0?

By mathematical convention, sequences typically start with the first term at position n = 1. This matches how we naturally count: 1st, 2nd, 3rd terms, not 0th, 1st, 2nd terms.

What if the problem asked for the 3rd term instead?

Simply substitute n = 3 into the formula! For $6n^2 - 1$ , you'd get $6(3)^2 - 1 = 6(9) - 1 = 53$ .

How do I know this formula gives a sequence and not just one number?

The variable n tells you it's a sequence! Each different value of n (1, 2, 3, 4...) produces a different term in the sequence.

Can sequence formulas have negative terms?

Absolutely! Depending on the formula and position n, terms can be positive, negative, or zero. Always calculate exactly what the formula gives you.

Do I need to simplify 6(1)² before subtracting 1?

Yes! Follow the order of operations: first calculate the exponent (1² = 1), then multiply (6 × 1 = 6), then subtract (6 - 1 = 5).

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