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

a is negative number.

b is negative number.

What is the sum of a+b?

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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