Find the Next Term in Arithmetic Sequence: -16, -22, -28, -34, ?

Q: Why is the common difference negative in this sequence?

The common difference is -6 because each term is smaller than the previous one. When sequences decrease, the common difference is always negative!

Q: How do I know if I calculated the common difference correctly?

Check that the same difference works for all consecutive pairs. In this sequence: -22-(-16)=-6, -28-(-22)=-6, -34-(-28)=-6. All equal -6!

Q: What if I get different differences between terms?

If the differences aren't the same, it's not an arithmetic sequence. Double-check your subtraction, especially with negative numbers. Remember: subtract the first from the second term.

Q: Can I use a formula instead of just adding the common difference?

Yes! The formula is $ a_n = a_1 + (n-1)d $. Here: $ a_5 = -16 + (5-1)(-6) = -16 + (-24) = -40 $

Q: How do I avoid making sign errors with negative numbers?

Be extra careful with parentheses! When you see -34 + (-6), think of it as -34 - 6 = -40. Practice writing out each step clearly.

Arithmetic Sequences with Negative Common Differences

$-16,-22,-28,-34,\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the next number in the sequence

00:05 Find all the numbers on the axis

00:15 Find the difference between each consecutive number

00:36 We can see that the difference is constant between each number

00:49 We'll use this difference to find the next number

01:15 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

$-16,-22,-28,-34,\text{?}$

Step-by-step solution

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

Step 1: Confirm the pattern in the sequence by calculating differences between terms.
Step 2: Calculate the next term in the sequence using the identified pattern.

Let's analyze the sequence $-16, -22, -28, -34$ :

Step 1: Calculate the difference between consecutive terms:
$-22 - (-16) = -6$
$-28 - (-22) = -6$
$-34 - (-28) = -6$
It is clear that the common difference, denoted as $d$ , is $-6$ .

Step 2: Add the common difference to the last term to find the next number:
The last number is $-34$ . Add the common difference $d = -6$ to find the next term:
$-34 + (-6) = -40$

Therefore, the next number in this sequence is $-40$ .

Final Answer

$-40$

Key Points to Remember

Essential concepts to master this topic

Pattern: Find common difference by subtracting consecutive terms
Technique: Calculate -22 - (-16) = -6, then verify with remaining terms
Check: Confirm pattern holds for all pairs: each difference equals -6 ✓

Common Mistakes

Avoid these frequent errors

Adding the common difference instead of subtracting when finding differences
Don't calculate -16 - (-22) = 6 instead of -22 - (-16) = -6! This gives you the wrong sign and direction. Always subtract the first term from the second term to find the common difference.

Practice Quiz

Test your knowledge with interactive questions

Solve the following expression:

$(+8)+(+12)=\text{ ?}$

FAQ

Everything you need to know about this question

Why is the common difference negative in this sequence?

The common difference is -6 because each term is smaller than the previous one. When sequences decrease, the common difference is always negative!

How do I know if I calculated the common difference correctly?

Check that the same difference works for all consecutive pairs. In this sequence: -22-(-16)=-6, -28-(-22)=-6, -34-(-28)=-6. All equal -6!

What if I get different differences between terms?

If the differences aren't the same, it's not an arithmetic sequence. Double-check your subtraction, especially with negative numbers. Remember: subtract the first from the second term.

Can I use a formula instead of just adding the common difference?

Yes! The formula is $a_n = a_1 + (n-1)d$ . Here: $a_5 = -16 + (5-1)(-6) = -16 + (-24) = -40$

How do I avoid making sign errors with negative numbers?

Be extra careful with parentheses! When you see -34 + (-6), think of it as -34 - 6 = -40. Practice writing out each step clearly.

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