Identify the Next Number: Arithmetic Sequence Pattern of 1800, 1700, 1600, 1500

Arithmetic Sequences with Negative Common Differences

Look at the sequence below:

... ,1800, 1700, 1600, 1500

Which of the following numbers will appear in the sequence of numbers indicated above?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find which number fits in the sequence?
00:03 Calculate the difference between each element
00:10 Find the pattern and continue calculating
00:17 This is the next element in the sequence, and we'll continue until we find the fitting number
00:29 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 sequence below:

... ,1800, 1700, 1600, 1500

Which of the following numbers will appear in the sequence of numbers indicated above?

2

Step-by-step solution

This sequence of numbers is an arithmetic sequence, characterized by a constantly decreasing pattern by 100. Let's start the sequence identification process:

The given terms are ..., 1800, 1700, 1600, 1500.

From this, we observe:

  • The common difference d d is 100-100.

One way to consider sequence patterns is based on the number-ending zeros repeatedly positioned as 00. By checking common divisibility differentials or inspecting values directly, we see matching with that mode.

Now, let's inspect each of the options:

  • Option 1: 1550 is not easily fitting with the visible sequence number pattern.

  • Option 2: 1890 does not conform precisely as non-integral multiples divide suspect differentially.

  • Option 3: 2000 was determined for matching preceding sequence confirmation tightly.

  • Option 4: 2150 also does not pair properly, nor sophisticated excessive multiples derive support.

Given the earlier assessment execution matched with insight into sequence direct scale or normal concept utilization, the available choice 2000 thus coincides with the known term, maintaining steady uniformity visible in sequence pattern components. Hence:

The correct choice is 20002000.

3

Final Answer

2000

Key Points to Remember

Essential concepts to master this topic
  • Pattern Recognition: Each term decreases by the same constant difference
  • Technique: Find common difference: 1700 - 1800 = -100
  • Check: Verify candidate fits pattern: 2000 - 100 = 1900, then 1800 ✓

Common Mistakes

Avoid these frequent errors
  • Testing numbers without finding the pattern first
    Don't just guess which answer 'looks right' without identifying the sequence rule = random wrong choices! This wastes time and misses the mathematical structure. Always find the common difference first, then check if candidates follow the pattern.

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 what number comes before 1800 in this sequence?

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Since the common difference is -100, work backwards: 1800 + 100 = 1900, then 1900 + 100 = 2000. So 2000 comes before 1800 in this sequence!

Why is 1550 wrong if it's between two given numbers?

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Being between sequence terms doesn't make a number part of the sequence! The pattern decreases by exactly 100 each time, so 1550 breaks this rule since 1600 - 1550 = 50, not 100.

Can arithmetic sequences go backwards like this one?

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Absolutely! When the common difference is negative (like -100), the sequence decreases. Think of it as counting backwards by the same amount each time.

How do I check if 2000 really belongs in this sequence?

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Start with 2000 and subtract 100 repeatedly: 2000 → 1900 → 1800 → 1700 → 1600 → 1500. Since this matches our given sequence, 2000 is correct!

What if I need to find a term that's not in the answer choices?

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Use the formula: an=a1+(n1)d a_n = a_1 + (n-1)d where d = -100. Find which term 2000 is, then use the formula to find any other term you need.

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