Solve the Sequence Formula n²-n: Finding the Fifth Element

Sequence Formulas with Substitution Method

Below is the rule for a sequence written in terms of n n :

n2−n n^2-n

What is the 5th element?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the 5th element
00:03 Position of the desired element according to the data
00:11 Substitute appropriate values according to the data and solve to find the element
00:18 Always solve exponents first
00:27 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Below is the rule for a sequence written in terms of n n :

n2−n n^2-n

What is the 5th element?

2

Step-by-step solution

To solve this problem, we will follow these steps:

  • Step 1: Understand the formula given for the sequence.
  • Step 2: Substitute n=5 n = 5 into the formula to find the 5th element.
  • Step 3: Simplify the expression to find the solution.

Now, let's work through each step:

Step 1: We have the formula for the sequence as an=n2−n a_n = n^2 - n .

Step 2: We will substitute n=5 n = 5 into the formula:

a5=52−5 a_5 = 5^2 - 5

Step 3: Calculate the expression:

a5=25−5 a_5 = 25 - 5

a5=20 a_5 = 20

Therefore, the 5th element of the sequence is 20 20 .

3

Final Answer

20 20

Key Points to Remember

Essential concepts to master this topic
  • Formula: Use an=n2−n a_n = n^2 - n where n is the position
  • Technique: Substitute n = 5: 52−5=25−5=20 5^2 - 5 = 25 - 5 = 20
  • Check: Verify by testing: position 5 gives 25−5=20 25 - 5 = 20 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing the position number with the sequence value
    Don't think the 5th element equals 5 = wrong understanding! The position (n = 5) is what you substitute into the formula, not the answer. Always substitute the position number into the given formula n2−n n^2 - n to find the actual sequence value.

Practice Quiz

Test your knowledge with interactive questions

Look at the following set of numbers and determine if there is any property, if so, what is it?

\( 94,96,98,100,102,104 \)

FAQ

Everything you need to know about this question

What does n2−n n^2 - n actually mean?

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This is the rule that tells you how to find any element in the sequence! The variable n represents the position number, so you substitute the position you want into this formula.

How do I find other elements like the 3rd or 7th?

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Use the same method! For the 3rd element: 32−3=9−3=6 3^2 - 3 = 9 - 3 = 6 . For the 7th element: 72−7=49−7=42 7^2 - 7 = 49 - 7 = 42 . Just substitute the position number for n!

Why do we calculate 52 5^2 first before subtracting?

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We follow the order of operations! Exponents come before subtraction, so 52=25 5^2 = 25 first, then 25−5=20 25 - 5 = 20 .

Can sequence formulas be more complicated than this?

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Yes! You might see formulas like 2n+3 2n + 3 , n3−2n n^3 - 2n , or nn+1 \frac{n}{n+1} . The method is always the same: substitute the position number and calculate!

What if I get a negative number as an answer?

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That's totally fine! Some sequences have negative values. For example, if you tried n=0 n = 0 in this formula: 02−0=0 0^2 - 0 = 0 , which is neither positive nor negative.

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