Find the Next Term in the Sequence: 1, 0, -1, -2, -3, -4, ?

Q: How do I know this is an arithmetic sequence?

Check if the difference between consecutive terms is the same. Here: $ 0-1 = -1 $, $ -1-0 = -1 $, $ -2-(-1) = -1 $. Since all differences equal $ -1 $, it's arithmetic!

Q: What if the common difference is negative?

That's perfectly normal! A negative common difference means the sequence is decreasing. Just add the negative difference: $ -4 + (-1) = -5 $.

Q: Can I use a formula instead of adding each time?

Yes! The formula is $ a_n = a_1 + (n-1)d $ where $ a_1 = 1 $ and $ d = -1 $. For the 7th term: $ a_7 = 1 + (7-1)(-1) = 1 - 6 = -5 $.

Q: How do I check my answer is correct?

Verify the pattern continues: $ 1, 0, -1, -2, -3, -4, -5 $. Each term should be exactly 1 less than the previous term. $ -4 - 1 = -5 $ ✓

Q: What if I see a different type of sequence?

Always start by checking for arithmetic patterns (constant differences) first. If that doesn't work, try geometric patterns (constant ratios) or look for other relationships between terms.

Arithmetic Sequences with Negative Common Differences

$1,0,-1,-2,-3,-4,\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 Let's find the missing term in this sequence.

00:13 We found two consecutive terms on the number line.

00:20 Notice how the progression is moving leftwards, indicating a decrease.

00:26 Let's calculate the difference between these terms.

00:32 We need to check if this difference stays the same for the other terms.

00:43 As we can see, the difference remains consistent between terms.

00:51 So, we'll apply this difference to find the next term.

00:58 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

$1,0,-1,-2,-3,-4,\text{?}$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the pattern present in the sequence.
The sequence provided is $1, 0, -1, -2, -3, -4$ .
Step 2: Recognize that each number is decreasing by 1.
This indicates an arithmetic sequence with a common difference of $-1$ .
Step 3: Determine the next number using the pattern.
Starting with $-4$ , subtract $1$ to find the next term.

Now, let's work through each step:
Step 1: The sequence starts at $1$ and each subsequent number decreases by $1$ .
Step 2: Identify this consistent decrease signifying an arithmetic sequence with a common difference $d = -1$ .
Step 3: Calculate the next term after $-4$ :
$-4 - 1 = -5$

Therefore, the next number in the sequence is $-5$ .

Final Answer

$-5$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Each term decreases by the same constant value
Formula: Next term = current term + common difference: $-4 + (-1) = -5$
Verification: Check differences between consecutive terms are all equal: $1-0 = 0-(-1) = -1$ ✓

Common Mistakes

Avoid these frequent errors

Assuming the pattern changes or gets more complex
Don't overthink simple sequences by looking for quadratic or other complex patterns = wrong next term! Students often miss that $1, 0, -1, -2, -3, -4$ simply decreases by 1 each time. Always check if consecutive differences are constant first.

Practice Quiz

Test your knowledge with interactive questions

a is negative number.

b is negative number.

What is the sum of a+b?

FAQ

Everything you need to know about this question

How do I know this is an arithmetic sequence?

Check if the difference between consecutive terms is the same. Here: $0-1 = -1$ , $-1-0 = -1$ , $-2-(-1) = -1$ . Since all differences equal $-1$ , it's arithmetic!

What if the common difference is negative?

That's perfectly normal! A negative common difference means the sequence is decreasing. Just add the negative difference: $-4 + (-1) = -5$ .

Can I use a formula instead of adding each time?

Yes! The formula is $a_n = a_1 + (n-1)d$ where $a_1 = 1$ and $d = -1$ . For the 7th term: $a_7 = 1 + (7-1)(-1) = 1 - 6 = -5$ .

How do I check my answer is correct?

Verify the pattern continues: $1, 0, -1, -2, -3, -4, -5$ . Each term should be exactly 1 less than the previous term. $-4 - 1 = -5$ ✓

What if I see a different type of sequence?

Always start by checking for arithmetic patterns (constant differences) first. If that doesn't work, try geometric patterns (constant ratios) or look for other relationships between terms.

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