Ascending Sequence Problem: Find First Positive in -10,-7, _, _, _

Q: How do I find the common difference in an arithmetic sequence?

Subtract the first term from the second term: $ d = -7 - (-10) = -7 + 10 = 3 $. The common difference is always the same between any two consecutive terms!

Q: What if I get confused with negative numbers?

Remember: negative numbers are still negative even when they're close to zero! -1 is still negative. Only numbers greater than zero are positive.

Q: Do I need to write out the entire sequence?

Not necessarily! You can use the formula $ a_n = a_1 + (n-1)d $ where a₁ = -10 and d = 3 to find any term directly.

Q: How do I know when to stop extending the sequence?

Keep adding the common difference until you get your first positive number. In this case: -10, -7, -4, -1, 2 - stop at 2 since it's positive!

Q: What if the common difference was negative?

If d is negative, the sequence decreases and may never become positive. Always check the sign of your common difference first!

Arithmetic Sequences with Negative Start

Look at the ascending sequence:

$-10, -7, \_ , \_ , \_$

Which element contains the first positive number?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the first positive element

00:04 Find the difference between each element

00:09 This is the sequence's pattern

00:15 Continue calculating sequence elements until we reach the positive element

00:30 This is the first positive element

00:37 Find its position in the sequence

00:45 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

Look at the ascending sequence:

$-10, -7, \_ , \_ , \_$

Which element contains the first positive number?

Step-by-step solution

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

Step 1: Identify the common difference between the given terms.
Step 2: Extend the sequence using this common difference.
Step 3: Determine when the first term turns positive and identify its position.

Let's proceed with the solution:

Step 1: The common difference $d$ can be calculated by subtracting the first term from the second term:
$d = -7 - (-10) = 3$ .

Step 2: Using this difference, we extend the sequence:
Third element: $-7 + 3 = -4$
Fourth element: $-4 + 3 = -1$
Fifth element: $-1 + 3 = 2$

Step 3: Check when the first positive number occurs:
The sequence becomes positive at the fifth element with the value $2$ .

Therefore, the solution to the problem is that the first positive number occurs at the Fifth element.

Final Answer

Fifth element

Key Points to Remember

Essential concepts to master this topic

Pattern: Find common difference by subtracting consecutive terms
Technique: Add d=3 repeatedly: -10, -7, -4, -1, 2
Check: Verify each term increases by same amount: 3 ✓

Common Mistakes

Avoid these frequent errors

Assuming the sequence becomes positive too early
Don't think -1 is positive = wrong position identified! Negative numbers are still negative even when close to zero. Always continue the pattern until you reach a number greater than zero.

Practice Quiz

Test your knowledge with interactive questions

Look at the following set of numbers and determine if there is any property, if so, what is it?

$$ 94,96,98,100,102,104 $$

FAQ

Everything you need to know about this question

How do I find the common difference in an arithmetic sequence?

Subtract the first term from the second term: $d = -7 - (-10) = -7 + 10 = 3$ . The common difference is always the same between any two consecutive terms!

What if I get confused with negative numbers?

Remember: negative numbers are still negative even when they're close to zero! -1 is still negative. Only numbers greater than zero are positive.

Do I need to write out the entire sequence?

Not necessarily! You can use the formula $a_n = a_1 + (n-1)d$ where a₁ = -10 and d = 3 to find any term directly.

How do I know when to stop extending the sequence?

Keep adding the common difference until you get your first positive number. In this case: -10, -7, -4, -1, 2 - stop at 2 since it's positive!

What if the common difference was negative?

If d is negative, the sequence decreases and may never become positive. Always check the sign of your common difference first!

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