Using the Formula 3n+5: Discover the 3rd Term

Q: What does n represent in the formula?

The variable n represents the position of the term in the sequence. So n = 1 for the first term, n = 2 for the second term, n = 3 for the third term, and so on.

Q: How do I find any term in this sequence?

Simply substitute the position number for n in the formula $ 3n + 5 $. For example, the 10th term would be $ 3(10) + 5 = 35 $.

Q: Can I list out the first few terms to check my work?

Absolutely! Calculate: 1st term = $ 3(1) + 5 = 8 $, 2nd term = $ 3(2) + 5 = 11 $, 3rd term = $ 3(3) + 5 = 14 $. This confirms our answer!

Q: What does the +5 do in this formula?

The +5 shifts every term up by 5. Without it, the sequence would be 3, 6, 9, 12... But with +5, it becomes 8, 11, 14, 17... starting higher and keeping the same pattern.

Sequence Formulas with Term Substitution

$3n+5$

What is the third term in the sequence above?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's find member number three.

00:10 Substitute the position in the formula. Then, let's solve it step by step.

00:23 Remember! Always do multiplication and division before addition and subtraction.

00:31 Great job! That's the solution to our question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$3n+5$

What is the third term in the sequence above?

Step-by-step solution

To find the third term in the sequence defined by $3n + 5$ , we follow these steps:

Step 1: Identify the term number we are interested in. We need the third term, so set $n = 3$ .
Step 2: Use the sequence formula $a_n = 3n + 5$ .
Step 3: Substitute $n = 3$ into the formula:

$a_3 = 3(3) + 5$

Step 4: Perform the arithmetic calculations:

$3(3) = 9$
Adding 5 gives $9 + 5 = 14$ .

Therefore, the third term in the sequence is $14$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Use $a_n = 3n + 5$ where n is the position
Technique: Substitute n = 3: $3(3) + 5 = 9 + 5 = 14$
Check: First term (n=1): 8, second term (n=2): 11, third term (n=3): 14 ✓

Common Mistakes

Avoid these frequent errors

Using the term value instead of position number
Don't substitute the term's value into n = wrong position! This confuses the term's position with its actual value. Always use n as the position number: for the 3rd term, use n = 3.

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. So n = 1 for the first term, n = 2 for the second term, n = 3 for the third term, and so on.

How do I find any term in this sequence?

Simply substitute the position number for n in the formula $3n + 5$ . For example, the 10th term would be $3(10) + 5 = 35$ .

What if I want to find which term equals a certain value?

Set the formula equal to that value and solve for n. For example, if you want the term that equals 20: $3n + 5 = 20$ , so $n = 5$ (the 5th term).

Can I list out the first few terms to check my work?

Absolutely! Calculate: 1st term = $3(1) + 5 = 8$ , 2nd term = $3(2) + 5 = 11$ , 3rd term = $3(3) + 5 = 14$ . This confirms our answer!

What does the +5 do in this formula?

The +5 shifts every term up by 5. Without it, the sequence would be 3, 6, 9, 12... But with +5, it becomes 8, 11, 14, 17... starting higher and keeping the same pattern.

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