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

00:00 Find the first term

00:03 Insert the position of the appropriate term in the formula and solve

00:16 Always solve multiplication and division before addition and subtraction

00:25 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 $6n-1$ .

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

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

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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