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

Arithmetic Sequences with Negative Start

Look at the ascending sequence:

10,7,_,_,_ -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
1

Understand the problem

Look at the ascending sequence:

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

Which element contains the first positive number?

2

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 d can be calculated by subtracting the first term from the second term:
d=7(10)=3 d = -7 - (-10) = 3 .

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

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

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

3

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

12 ☐ 10 ☐ 8 7 6 5 4 3 2 1

Which numbers are missing from the sequence so that the sequence has a term-to-term rule?

FAQ

Everything you need to know about this question

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

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Subtract the first term from the second term: d=7(10)=7+10=3 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?

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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?

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Not necessarily! You can use the formula an=a1+(n1)d 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?

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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?

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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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