Determine the Next Number in the Arithmetic Sequence: -6, -3, 0, 3, 6, ?

Video Solution

Solution Steps

00:07 Let's complete the next element in our sequence.

00:11 Observe how all the elements are placed on the number line.

00:23 Notice the change between each element on the line.

00:41 We see the sequence is increasing by adding three each time.

00:56 Using this pattern, let's find the next element together.

01:05 And that's how we solve the problem. Great job!

Step-by-Step Solution

To solve this problem, we will examine the differences between consecutive terms in the given sequence:
The sequence is $-6, -3, 0, 3, 6$ .

Step 1: Find the difference between consecutive terms.
- From $-6$ to $-3$ : $-3 - (-6) = 3$
- From $-3$ to $0$ : $0 - (-3) = 3$
- From $0$ to $3$ : $3 - 0 = 3$
- From $3$ to $6$ : $6 - 3 = 3$
Step 2: Verify that the difference is consistent. The common difference $d$ is $3$ .
Step 3: Use the common difference to find the next term in the sequence:
From $6$ , add the common difference ( $3$ ): $6 + 3 = 9$ .

Therefore, the next number in the sequence is $9$ .

This matches choice 3 in the provided answer choices.