Calculate Values: Finding Terms 10-12 in the Expression 5n-3

Q: How do I remember the formula 5n-3?

Think of it as: multiply the position by 5, then subtract 3. So for the 10th term, you do 5 × 10 - 3. The pattern is always the same!

Q: What if I get confused about which term is which?

Write it out clearly: $ a_{10} $ means "the 10th term", so substitute n=10. Use subscripts or labels like "Term 10:" to keep track of your work.

Q: Can I use this formula for any term number?

Yes! The formula $ 5n-3 $ works for any positive integer n. For the 100th term, just calculate $ 5(100)-3 = 497 $.

Q: How do I check if my calculation is right?

Substitute your answer back into the formula! If $ a_{12} = 57 $, then $ 5(12)-3 = 60-3 = 57 $ ✓. The math should work both ways.

Sequence Evaluation with Consecutive Terms

For the series $5n-3$

Complete the equation with the numeric element 10 up to 12.

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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 of the series

00:04 We'll substitute the appropriate member position in the series formula and solve

00:11 Substitute N = 10 in the series formula and solve to find the member

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

00:27 This is the 10th member in the series

00:30 We'll use the same method to find members 11 and 12

00:34 Substitute N = 11 in the series formula and solve to find the member

00:44 This is the 11th member

00:50 Substitute N = 12 in the series formula and solve to find the member

01:08 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

For the series $5n-3$

Complete the equation with the numeric element 10 up to 12.

Step-by-step solution

To solve this problem, we need to follow these steps:

Step 1: Substitute $n = 10$ into the sequence formula to find the term.
Using the formula $a_n = 5n - 3$ , replace $n$ with 10:
$a_{10} = 5 \times 10 - 3 = 50 - 3 = 47$ .
Step 2: Substitute $n = 11$ into the sequence formula to find the term.
Using the formula $a_n = 5n - 3$ , replace $n$ with 11:
$a_{11} = 5 \times 11 - 3 = 55 - 3 = 52$ .
Step 3: Substitute $n = 12$ into the sequence formula to find the term.
Using the formula $a_n = 5n - 3$ , replace $n$ with 12:
$a_{12} = 5 \times 12 - 3 = 60 - 3 = 57$ .

Therefore, the sequence terms when $n = 10, 11, 12$ are: 57, 52, 47.

Final Answer

57 , 52 , 47

Key Points to Remember

Essential concepts to master this topic

Formula Application: Substitute each n-value into 5n-3 separately
Technique: For n=12: 5(12)-3 = 60-3 = 57
Check: Verify by calculating backwards: 57+3 = 60 ÷ 5 = 12 ✓

Common Mistakes

Avoid these frequent errors

Calculating terms in wrong order
Don't assume terms increase as n increases = backwards sequence! With 5n-3, larger n gives larger terms, so a₁₀ = 47, a₁₁ = 52, a₁₂ = 57. Always calculate each term individually and list in proper order.

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

Why don't the terms go in ascending order like 47, 52, 57?

The question asks for terms 10, 11, 12 in that specific order! Since $a_{10} = 47$ , $a_{11} = 52$ , and $a_{12} = 57$ , the answer is 47, 52, 57 when listed as requested.

How do I remember the formula 5n-3?

Think of it as: multiply the position by 5, then subtract 3. So for the 10th term, you do 5 × 10 - 3. The pattern is always the same!

What if I get confused about which term is which?

Write it out clearly: $a_{10}$ means "the 10th term", so substitute n=10. Use subscripts or labels like "Term 10:" to keep track of your work.

Can I use this formula for any term number?

Yes! The formula $5n-3$ works for any positive integer n. For the 100th term, just calculate $5(100)-3 = 497$ .

How do I check if my calculation is right?

Substitute your answer back into the formula! If $a_{12} = 57$ , then $5(12)-3 = 60-3 = 57$ ✓. The math should work both ways.

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