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

Question

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

What is the first term?

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

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 $\boxed{5}$ .