Explain the pattern rule.
a) -2,4,-8,16,-32
b) -15,30,90,-360
a) The pattern rule for the sequence -2, 4, -8, 16, -32 is that each term is obtained by multiplying the previous term by -2. So, we start with -2, then multiply by -2 to get 4, then multiply 4 by -2 to get -8, and so on. It's a bit like playing a game of "how low can you go" but with negative numbers!
b) Oh boy, this one's a real doozy! The pattern rule for the sequence -15, 30, 90, -360 is that each term is obtained by multiplying the previous term by -2 and then adding some extra oomph. So, we start with -15, then we multiply it by -2 to get 30, but wait, it doesn't stop there! We then add some extra flavor to the mix to get 90. And just when you thought you had it all figured out, we multiply 90 by -2 and sprinkle in some more pizzazz to end up with -360. It's like a math equation gone wild, dancing to its own funky beat!
a) To find the pattern rule for the sequence -2, 4, -8, 16, -32, we can observe that each number is obtained by multiplying the previous number by -2.
So, the rule for this sequence is: multiply each term by -2 to get the next term.
b) To find the pattern rule for the sequence -15, 30, 90, -360, we can see that each number is obtained by multiplying the previous number by -2 and then by 3.
So, the rule for this sequence is: multiply each term by -2 and then by 3 to get the next term.
To find the pattern rule for a sequence of numbers, we need to analyze the relationship between the terms in the sequence. Let's look at each sequence individually:
a) -2, 4, -8, 16, -32
If we examine the pattern between consecutive terms, we can observe that each term is obtained by multiplying the previous term by -2.
Here's the breakdown:
-2 * -1 = 4
4 * -2 = -8
-8 * -2 = 16
16 * -2 = -32
So, the pattern rule for this sequence is to multiply each term by -2 to get the next term.
b) -15, 30, 90, -360
For this sequence, the pattern rule is not as straightforward. Let's analyze the relationship between the terms:
To get from -15 to 30, we can observe that we multiply by -2.
To get from 30 to 90, we multiply by 3.
To get from 90 to -360, we multiply by -4.
So, to find the next term, we need to consider the previous term and multiply by the next number in the sequence: -2, 3, -4.
Using this pattern rule, we can find the following terms:
-360 * (-2) = 720
720 * 3 = 2160
2160 * (-4) = -8640
Therefore, the pattern rule for this sequence is to multiply each term by the corresponding number in the sequence -2, 3, -4.
By observing the pattern and analyzing the relationships between the terms, we can determine the pattern rule for any given sequence of numbers.
(a) each number is -2 times the previous
(b) I suspect a typo, since the signs do not alternate. However, a rule which works is that the nth term is n times the previous term, with sign changing when (n-1) is a multiple of 3.