Calculate the Fourth Term in the Sequence 5n-5

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

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

Q: Why do we get 0 for the first term?

When n = 1: $ 5(1) - 5 = 0 $. This is correct! Sequences can start with zero or negative numbers. The formula determines what each term equals.

Q: What if I need the 10th term?

Use the same method! Substitute n = 10 into the formula: $ 5(10) - 5 = 45 $. The formula works for any term position.

Q: Is this an arithmetic sequence?

Yes! Each term increases by 5 (the coefficient of n). The sequence goes: 0, 5, 10, 15, 20... with a common difference of 5.

Arithmetic Sequences with Substitution Method

$5n-5$

What is the fourth term in the sequence above?

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Step-by-step video solution

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00:00 Find member 4

00:04 Insert the corresponding member's position in the formula and solve

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

00:22 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

$5n-5$

What is the fourth term in the sequence above?

Step-by-step solution

To solve this problem, we need to determine the fourth term in the sequence given by the expression $5n - 5$ .

Step 1: Identify the term's position
The problem asks for the fourth term, which means we need to find $a_4$ where the term number $n = 4$ .

Step 2: Substitute the position into the sequence formula
Using the formula for the sequence, $a_n = 5n - 5$ , we substitute $n = 4$ into the expression:

$a_4 = 5(4) - 5$

Step 3: Simplify the expression
Now, we calculate:

$a_4 = 20 - 5 = 15$

Therefore, the fourth term in the sequence is $15$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Use $a_n = 5n - 5$ where n represents term position
Technique: Substitute n = 4 to get $5(4) - 5 = 15$
Check: Verify by calculating first few terms: 0, 5, 10, 15 ✓

Common Mistakes

Avoid these frequent errors

Using wrong position number for the term
Don't substitute n = 3 when finding the fourth term = getting 10 instead of 15! Students often confuse term position with the term value. Always use the exact position number: fourth term means n = 4.

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 the 'n' represent in the formula?

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

Why do we get 0 for the first term?

When n = 1: $5(1) - 5 = 0$ . This is correct! Sequences can start with zero or negative numbers. The formula determines what each term equals.

How can I check if my answer is right?

Calculate a few terms in order: n=1 gives 0, n=2 gives 5, n=3 gives 10, n=4 gives 15. Each term increases by 5, which matches the pattern!

What if I need the 10th term?

Use the same method! Substitute n = 10 into the formula: $5(10) - 5 = 45$ . The formula works for any term position.

Is this an arithmetic sequence?

Yes! Each term increases by 5 (the coefficient of n). The sequence goes: 0, 5, 10, 15, 20... with a common difference of 5.

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