SOLUTION: WRITING RULES: Write the next term in the sequence. Then write a rule for the nth term. -5, 10, -15, 20, . . . (I understand that the sequence is multiples of 5, but I don't und

Question 951201: WRITING RULES: Write the next term in the sequence. Then write a rule for the nth term.
-5, 10, -15, 20, . . .
(I understand that the sequence is multiples of 5, but I don't understand how they got the negative for every other number) THANKS!! :D :3
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The multiples of 5 can be represented by the expression where is a whole number

Ex: if , then

How do we alternate the signs? We introduce the term . If n is even, then (ie positive 1). If n is odd, then . There are no other outcomes for this piece. So this is why is the perfect thing to tack on to help alternate the signs.

The nth term is . Notice how I am multiplying by

To confirm this, let's plug in n = 2 to get .

Now let's plug in n = 3 to get .

I'll let you check the others.

The next term is -25 as I'm sure you've already figured that out. Let's use n = 5 to confirm

.
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