Complete the Decimal Sequence: Finding Next Terms After 0, 0.2, 0.4, 0.6

Question

Complete the following sequence:

0,0.2,0.4,0.6,?,? 0,0.2,0.4,0.6,?,\text{?}

Video Solution

Solution Steps

00:00 Complete the sequence
00:07 Subtract between the numbers to find the difference
00:27 This is the difference between terms
00:34 Let's verify the pattern holds, subtract between the following numbers
01:01 We see the difference is equal, so the pattern holds
01:18 Let's use this pattern and add the difference to find the next term
01:46 This is the next term, let's use the same method for the remaining terms
02:25 And this is the solution to the question

Step-by-Step Solution

To determine the next numbers in the sequence 0,0.2,0.4,0.6 0, 0.2, 0.4, 0.6 , we proceed by identifying the pattern:

  • Evaluate the difference between the first two terms: 0.20=0.2 0.2 - 0 = 0.2 .
  • Verify this difference remains the same between the subsequent terms: 0.40.2=0.2 0.4 - 0.2 = 0.2 and 0.60.4=0.2 0.6 - 0.4 = 0.2 .

Each term increases by 0.2 0.2 . Therefore, this sequence follows an arithmetic progression with a common difference of 0.2 0.2 .

To find the next term in the sequence: add 0.2 0.2 to the last known term.

  • Next term after 0.6 0.6 is 0.6+0.2=0.8 0.6 + 0.2 = 0.8 .
  • To find the term following 0.8 0.8 , add 0.2 0.2 again: 0.8+0.2=1 0.8 + 0.2 = 1 .

Thus, the next two numbers in the sequence are 0.8 0.8 and 1 1 .

The correct answer, therefore, is 0.8,1 0.8, 1 .

Answer

0.8,1 0.8,1