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

Video Solution

Solution Steps

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 Solution

To solve this problem, follow these steps:

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

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

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 $2 - (-3)$ :

$? = 2 + 3 = 5$ .

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

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