Find the Next Term in Arithmetic Sequence: -15, -17, -19, -21, ?

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

The common difference is negative because each term is smaller than the previous one. When numbers decrease, we subtract a positive amount, which is the same as adding a negative number!

Q: How do I know if I found the right common difference?

Check that the same difference works between all consecutive pairs. Here: $ -17-(-15) = -2 $, $ -19-(-17) = -2 $, and $ -21-(-19) = -2 $.

Q: What if I get confused with the negative signs?

Remember: subtracting a negative is the same as adding! So $ -17 - (-15) = -17 + 15 = -2 $. Take your time with the arithmetic.

Q: Can I use a formula instead of finding the pattern?

Yes! The formula is $ a_n = a_1 + (n-1)d $, where $ a_1 = -15 $ and $ d = -2 $. But understanding the pattern helps you catch mistakes!

Q: How do I find the 10th term in this sequence?

Use the formula: $ a_{10} = -15 + (10-1)(-2) = -15 + 9(-2) = -15 - 18 = -33 $. Or count: start at -15 and subtract 2 nine times!

Arithmetic Sequences with Negative Common Differences

$-15,-17,-19,-21,\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's complete the next number in the sequence.

00:12 First, find all the numbers given on the axis.

00:17 Now, find the difference between each consecutive number.

00:27 Notice, the difference is constant between each number.

00:39 Use this difference to calculate the next number.

00:48 And that's the solution! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-15,-17,-19,-21,\text{?}$

Step-by-step solution

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

Step 1: Identify the pattern in the sequence.
Step 2: Calculate the common difference.
Step 3: Use the common difference to find the next term in the sequence.

Step 1: Look at the given sequence: $-15, -17, -19, -21$ .
To find the common difference, we can subtract each term from the next one. For example, the difference between $-15$ and $-17$ is:

$-17 - (-15) = -17 + 15 = -2$

Similarly, between $-17$ and $-19$ , and $-19$ and $-21$ , we have:

$-19 - (-17) = -2$

$-21 - (-19) = -2$

Step 2: We have determined that the common difference $d$ is $-2$ .

Step 3: To find the next term, subtract the common difference from the last term: $-21 - 2 = -23$ .

Therefore, the next number in the sequence is $-23$ .

Final Answer

$-23$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find the common difference between consecutive terms
Technique: Calculate $-17 - (-15) = -2$ for each pair
Check: Verify pattern holds: $-15, -17, -19, -21, -23$ all differ by -2 ✓

Common Mistakes

Avoid these frequent errors

Adding instead of subtracting the common difference
Don't add 2 to get -21 + 2 = -19! This reverses the sequence direction and gives wrong answers. Always subtract the common difference when it's negative: -21 + (-2) = -23.

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 negative because each term is smaller than the previous one. When numbers decrease, we subtract a positive amount, which is the same as adding a negative number!

How do I know if I found the right common difference?

Check that the same difference works between all consecutive pairs. Here: $-17-(-15) = -2$ , $-19-(-17) = -2$ , and $-21-(-19) = -2$ .

What if I get confused with the negative signs?

Remember: subtracting a negative is the same as adding! So $-17 - (-15) = -17 + 15 = -2$ . Take your time with the arithmetic.

Can I use a formula instead of finding the pattern?

Yes! The formula is $a_n = a_1 + (n-1)d$ , where $a_1 = -15$ and $d = -2$ . But understanding the pattern helps you catch mistakes!

How do I find the 10th term in this sequence?

Use the formula: $a_{10} = -15 + (10-1)(-2) = -15 + 9(-2) = -15 - 18 = -33$ . Or count: start at -15 and subtract 2 nine times!

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