Complete the Arithmetic Sequence: 10, -10, -30, ?

Video Solution

Solution Steps

00:06 Let's find the missing number in the sequence.

00:09 First, pick any two numbers that are next to each other.

00:13 Next, calculate the difference between these two numbers.

00:26 Check if this difference is the same for the next pair of numbers.

00:38 Since the difference is consistent, we can use it to find the next number in the sequence.

00:52 And that's how you solve the problem!

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Now, let's work through each step:

Step 1: Calculate the difference between the first and second terms $10$ and $-10$ :

The calculation is: $10 - (-10) = 10 + 10 = 20$ .

Step 2: Calculate the difference between the second term $-10$ and the third term $-30$ :

The calculation is: $-10 - (-30) = -10 + 30 = 20$ .

Step 3: Notice the pattern; each difference is $20$ . The series decreases by $20$ each time.

Step 4: Apply this consistency to determine the next number in the sequence:

Calculate the difference from the third number $-30$ :
$-30 - 20 = -50$ .

Therefore, the missing number is $\mathbf{-50}$ , which corresponds to choice $4$ .

Thus, the solution to the problem is $-50$ .