Pattern: Absolute value increases by 1 and the sign alternates Next Two Numbers: - 6, 7
Practice makes perfect
We will begin by finding the pattern. Then, we will be able to find the next two numbers.
Finding the Pattern
By observing the given sequence, we can see that there is no common difference nor common ratio.
1- 3 →- 2+5 →3- 7 →- 4+9 →5
1*(- 2) ⟶- 2*(- 23) ⟶3*(- 43) ⟶- 4*(- 54) ⟶5
This means that we have to take a different approach. First, note that the signs alternate from positive to negative.
1, -2, 3, -4, 5, ...
Next, we can tell that the absolute value of each number is one greater than the absolute value of the previous number.
Numbers in the sequence:& 1, - 2, 3, - 4, 5
Absolute values:& 1, 2, 3, 4, 5
Finally, we can describe the pattern.
The absolute value of each number in the list is one greater than the absolute value of the previous number in the list.
The signs alternate from positive to negative.
Finding the Terms
Let's use the pattern to find the next two numbers. Since the absolute value of 5 is 5, the absolute value of the next number must be 6. Thus, there are two options.
- 6 or 6
We also know that the next number has to be negative because 5 is positive. Therefore, the number that comes after 5 in this sequence is - 6. Following the same reasoning, we can tell that the number that comes after -6 is 7.
1, - 2, 3, - 4, 5, - 6, 7, ...
