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

Video Solution

Solution Steps

00:00 Complete the missing term in the sequence

00:03 Find 2 consecutive terms on the axis

00:07 Find the difference between the terms

00:20 Verify that this difference also holds between the next terms

00:32 We see that the difference is constant, so we'll use it to find the next term

00:46 And this is the solution to the question

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 $-50$ .