Answer:
-15, 20
Explanation:
To solve this problem we must first understand what the pattern is in the sequence. Once we understand the pattern, we can then apply it to the final known term to find the next two terms.
Take a look at the sequence given:
5, -5, 10, -10, 15,...
Let's start by figuring out how they got the second term in the sequence. To do that, identify what basic operation and number must be applied. This will reveal the pattern.
5 - first term
-5 - second term
5 ? ? = -5
5 × -1 = -5
So, this means the sequence multiplied negative one by the first term to get the second term. Therefore, the pattern should be 'multiply negative one' to get the next term. Just to be sure the pattern we found is correct, apply it to the given sequence.
5, -5, 10, -10, 15,...
5 × -1 = -5 [correct; provides the next term]
-5 × -1 = 5 [incorrect; does not provide the next term]
10 × -1 = -10 [correct; provides the next term]
-10 × -1 = 10 [incorrect; does not provide the next term]
According to the calculations shown above, the pattern we have identified ('multiply negative one') only works on every other term. Therefore, we must figure out the rest of the pattern for the remaining terms. To do that, identify what basic operation and number must be applied.
-5 - second term
10 - third term
-5 ? ? = 10
-5 × -2 = 10
So, this means the sequence multiplies negative two every other term. Therefore, the pattern should be:
multiply by negative one, multiply by negative two
However, to be sure the pattern we have identified is correct, apply it to the sequence.
5 × -1 = -5 [correct; provides the next term]
-5 × -2 = 10 [correct; provides the next term]
10 × -1 = -10 [correct; provides the next term]
-10 × -2 = 15 [correct; provides the next term]
Now that we have identified the correct pattern, let's apply it to the last term to find the next two terms.
5, -5, 10, -10, 15....
15 × -1 = -15
-15 × -2 = 20
Therefore, the next two terms in the sequence is -15, 20.
