Find the Missing First Term in Sequence: ?, 2, -1, -4, -7, -10

?,2,1,4,7,10 ?,2,-1,-4,-7,-10

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Complete the next term
00:03 Let's examine all terms on the number line
00:10 Let's observe the change between consecutive terms
00:15 We can see the sequence is increasing, and the change is adding 3
00:37 Therefore, using this pattern we'll find the next term
00:46 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

?,2,1,4,7,10 ?,2,-1,-4,-7,-10

2

Step-by-step solution

To solve this problem, follow these steps:

  • Step 1: Determine the common difference d d of the sequence.
    The sequence given is 2,1,4,7,10 2, -1, -4, -7, -10 . Calculate the difference between consecutive terms:

d=12=3 d = -1 - 2 = -3 (confirming 4(1)=3,7(4)=3,10(7)=3 -4 - (-1) = -3, -7 - (-4) = -3, -10 - (-7) = -3 ).

  • Step 2: Use the common difference to find the term before the first known term (2).

We subtract the common difference from the first known term to find the missing term before it:
The first known term is 2. Calculate 2(3) 2 - (-3) :

?=2+3=5 ? = 2 + 3 = 5 .

Therefore, the first term of the sequence is 5\boxed{5}.

Reviewing the multiple-choice options, the correct choice is 5\boxed{5}, which corresponds to choice (3): 5 5 .

3

Final Answer

5 5

Practice Quiz

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Is there a term-to-term rule for the sequence below?

18 , 22 , 26 , 30

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