Complete the Arithmetic Sequence: Finding Missing Terms in 60, 50, ..., 30

Complete the sequence:

60,50,30, 60,50,\ldots30,\ldots

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Step-by-step written solution

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1

Understand the problem

Complete the sequence:

60,50,30, 60,50,\ldots30,\ldots

2

Step-by-step solution

To solve this problem, we will identify and use the pattern within the given sequence:

  • Step 1: Start with the given numbers 60 60 and 50 50 .
  • Step 2: Calculate the difference between these two numbers. We have 6050=10 60 - 50 = 10 .
  • Step 3: Assume this difference will continue throughout the sequence. This assumption is necessary because it suggests a common arithmetic sequence structure.

Following these steps, we can complete the sequence:

First term is 60 60 .

Second term is 50 50 .

Based on the assumption of an arithmetic sequence with a common difference of 10 -10 :

Third term: 5010=40 50 - 10 = 40 .

Fourth term: 4010=30 40 - 10 = 30 .

Continuing this pattern:
Fifth term: 3010=20 30 - 10 = 20 .
Sixth term: 2010=10 20 - 10 = 10 .

Therefore, the complete sequence is 60,50,40,30,20,10 60, 50, 40, 30, 20, 10 .

3

Final Answer

60,50,40,30,20,10 60,50,40,30,20,10

Practice Quiz

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Complete the following sequence:

\( 20,\ldots,24,26\ldots ,\ldots \)

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