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

Question

Look at the sequence below:

... ,1800, 1700, 1600, 1500

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

Video Solution

Solution Steps

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 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.

Answer

2000