Calculate the 10th to 12th Terms of the Sequence: Applying 5n - 3

Q: What does the 'n' represent in the formula?

The n represents the position number of the term in the sequence. For the 10th term, n = 10. For the 11th term, n = 11, and so on!

Q: Is this considered an arithmetic sequence?

Yes! This is an arithmetic sequence because there's a constant difference of 5 between consecutive terms. The general form is $ a_n = a_1 + (n-1)d $ where d = 5.

Arithmetic Sequences with Position Formula

For the series $5n-3$

What are the 10th up to the 12th elements?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find members 10,11,12

00:04 Let's substitute the desired member's position in the sequence formula and solve

00:24 Always solve multiplication and division before addition and subtraction

00:29 This is the 10th member in the sequence

00:32 We'll use the same method to find the next members

00:36 Let's substitute the desired member's position in the sequence formula and solve

00:50 Always solve multiplication and division before addition and subtraction

01:00 This is the 11th member in the sequence

01:07 Let's substitute the desired member's position in the sequence formula and solve

01:17 Always solve multiplication and division before addition and subtraction

01:23 And this is the solution to the question

Step-by-step written solution

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Understand the problem

For the series $5n-3$

What are the 10th up to the 12th elements?

Step-by-step solution

To solve this problem, we'll evaluate each term using the sequence formula:

Step 1: Calculate the 10th term.
Substitute $n = 10$ into the formula $a_n = 5n - 3$ :
$a_{10} = 5(10) - 3 = 50 - 3 = 47$ .
Step 2: Calculate the 11th term.
Substitute $n = 11$ into the formula $a_n = 5n - 3$ :
$a_{11} = 5(11) - 3 = 55 - 3 = 52$ .
Step 3: Calculate the 12th term.
Substitute $n = 12$ into the formula $a_n = 5n - 3$ :
$a_{12} = 5(12) - 3 = 60 - 3 = 57$ .

Therefore, the 10th, 11th, and 12th elements of the sequence are $47, 52,$ and $57$ respectively.

Final Answer

47,52,57

Key Points to Remember

Essential concepts to master this topic

Formula: Use $a_n = 5n - 3$ where n is position number
Technique: Substitute each position: $a_{10} = 5(10) - 3 = 47$
Check: Verify pattern: consecutive terms differ by 5 (52-47=5, 57-52=5) ✓

Common Mistakes

Avoid these frequent errors

Using wrong position numbers
Don't confuse term position with term value = wrong calculations! Students often substitute the wrong n-value or mix up which term they're finding. Always double-check that n matches the position you want (10th term means n=10).

Practice Quiz

Test your knowledge with interactive questions

Is there a term-to-term rule for the sequence below?

18 , 22 , 26 , 30

FAQ

Everything you need to know about this question

What does the 'n' represent in the formula?

The n represents the position number of the term in the sequence. For the 10th term, n = 10. For the 11th term, n = 11, and so on!

Why do we subtract 3 in this formula?

The -3 shifts the entire sequence down by 3 units. Without it, the formula would be $5n$ , giving us 5, 10, 15, 20... Instead, we get 2, 7, 12, 17...

How can I check if my answers are correct?

Substitute your answers back into the original formula! For example: $a_{10} = 5(10) - 3 = 47$ . Also check that consecutive terms have a common difference of 5.

What if I need to find many terms at once?

Use the same process for each term! Just substitute the position number (n) into $5n - 3$ . You can also use the common difference pattern: add 5 to get the next term.

Is this considered an arithmetic sequence?

Yes! This is an arithmetic sequence because there's a constant difference of 5 between consecutive terms. The general form is $a_n = a_1 + (n-1)d$ where d = 5.

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