Find the First Term Using the Sequence Formula 6n-1

Q: How can I find other terms in this sequence?

Just substitute different values of n! For example:Second term: $ 6(2) - 1 = 11 $Third term: $ 6(3) - 1 = 17 $Fourth term: $ 6(4) - 1 = 23 $

Sequence Formula with Position Variable

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

What is the first term in the sequence?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 First, let's find the first term in the sequence.

00:10 Next, place the term's position into the formula. Then, solve it step by step.

00:22 Remember to do multiplication and division before addition and subtraction.

00:31 And that's how we find the solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

What is the first term in the sequence?

Step-by-step solution

To determine the first term in the sequence, we must evaluate the expression $6n - 1$ at $n = 1$ since $n$ typically starts at 1 for sequences:

Step 1: Substitute $n = 1$ into $6n - 1$ .
Step 2: Compute $6 \times 1 - 1$ .
Step 3: Simplify the expression: $6 \times 1 = 6$ .
Step 4: Subtract 1 from 6, giving us 5.

Therefore, the first term in the sequence is $5$ .

Upon reviewing the answer choices, the correct choice is:
Choice 1: 5

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: For first term, substitute n = 1 into formula
Technique: Calculate 6(1) - 1 = 6 - 1 = 5
Check: Verify by computing next terms: second term is 6(2) - 1 = 11 ✓

Common Mistakes

Avoid these frequent errors

Using n = 0 for the first term
Don't substitute n = 0 thinking it's the starting point = wrong first term! For most sequences, position counting starts at n = 1, not zero. Always use n = 1 for the first term unless specifically told otherwise.

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?

In most sequences, we start counting positions from 1, not 0. So the first term is at position n = 1, second term at n = 2, and so on. This is the standard convention unless stated otherwise.

What if the sequence started at n = 0?

If a problem specifically states the sequence starts at n = 0, then use that! But most sequences start at n = 1. Always read the problem carefully for any special instructions.

How can I find other terms in this sequence?

Just substitute different values of n! For example:

Second term: $6(2) - 1 = 11$
Third term: $6(3) - 1 = 17$
Fourth term: $6(4) - 1 = 23$

What does the formula 6n - 1 tell me about the sequence?

This formula shows that each term increases by 6 from the previous term. It's an arithmetic sequence with first term 5 and common difference 6.

How do I check if my answer is correct?

Calculate a few terms to see if they make sense! If your first term is 5, then the second should be 11, third should be 17, etc. Each term should be 6 more than the previous one.

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