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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Look at the sequence below:
... ,1800, 1700, 1600, 1500
Which of the following numbers will appear in the sequence of numbers indicated above?
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 is .
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 .
2000
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?
Since the common difference is -100, work backwards: 1800 + 100 = 1900, then 1900 + 100 = 2000. So 2000 comes before 1800 in this sequence!
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.
Absolutely! When the common difference is negative (like -100), the sequence decreases. Think of it as counting backwards by the same amount each time.
Start with 2000 and subtract 100 repeatedly: 2000 → 1900 → 1800 → 1700 → 1600 → 1500. Since this matches our given sequence, 2000 is correct!
Use the formula: where d = -100. Find which term 2000 is, then use the formula to find any other term you need.
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