Solve the Sequence Equation: Is 1 a Term in 15n - 20?

Q: Why can't n be a fraction in sequences?

In sequences, n represents the position of a term (1st term, 2nd term, etc.). You can't have the 7/5th term - positions must be whole numbers!

Q: How do I check if any number is in this sequence?

Set $ 15n - 20 = \text{your number} $ and solve for n. If n is a positive integer, then yes! If n is negative, zero, or fractional, then no.

Q: Can I just plug in numbers to check?

You could, but that's inefficient! Setting up an equation like $ 15n - 20 = 1 $ gives you the exact answer much faster than guessing.

Linear Sequences with Integer Solutions

$15n-20$

Is the number 1 a term in the sequence above?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Is number 1 part of the sequence?

00:10 Let's plug the number into the sequence formula and solve for N.

00:15 If N is a positive whole number, then it's the position in the sequence.

00:22 Now, let's isolate N in the equation.

00:34 N is positive but not a whole number. So, the number is not part of the sequence.

00:41 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$15n-20$

Is the number 1 a term in the sequence above?

Step-by-step solution

To determine if the number 1 is a term in the sequence given by $15n - 20$ , we set the expression equal to 1:

$15n - 20 = 1$

Now, solve for $n$ :

$15n - 20 + 20 = 1 + 20$
$15n = 21$

Divide both sides by 15 to solve for $n$ :

$n = \frac{21}{15}$

Simplify the fraction:

$n = \frac{7}{5}$

The result, $n = \frac{7}{5}$ , is not an integer. Since $n$ must be a positive integer in sequence indexing, there is no valid solution for integer $n$ . Therefore, the number 1 cannot be a term of this sequence.

The correct answer is No.

Final Answer

No.

Key Points to Remember

Essential concepts to master this topic

Sequence Terms: n must be a positive integer for valid terms
Technique: Set 15n - 20 = 1 and solve: n = 21/15 = 7/5
Check: Since 7/5 is not an integer, 1 cannot be a term ✓

Common Mistakes

Avoid these frequent errors

Accepting fractional values for n in sequences
Don't say 'yes' just because you can solve 15n - 20 = 1 to get n = 7/5! Fractional n values don't make sense for sequence positions. Always remember that n must be a positive integer (1, 2, 3, ...) to represent actual terms in a sequence.

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 can't n be a fraction in sequences?

In sequences, n represents the position of a term (1st term, 2nd term, etc.). You can't have the 7/5th term - positions must be whole numbers!

What if I get a decimal when solving for n?

If n comes out as a decimal or fraction, the number you're testing cannot be a term in the sequence. Only integer solutions for n produce valid sequence terms.

How do I check if any number is in this sequence?

Set $15n - 20 = \text{your number}$ and solve for n. If n is a positive integer, then yes! If n is negative, zero, or fractional, then no.

What numbers ARE in the sequence 15n - 20?

Substitute positive integers: n=1 gives -5, n=2 gives 10, n=3 gives 25, etc. The sequence is -5, 10, 25, 40, 55...

Can I just plug in numbers to check?

You could, but that's inefficient! Setting up an equation like $15n - 20 = 1$ gives you the exact answer much faster than guessing.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Series questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime