Tell whether the sequence is arithmetic. If the sequence is arithmetic, write a function rule to represent it.
12, –9, 6, –3, ...
since the terms alternate between positive and negative there is no way there can be a constant difference between terms. So, NOT arithmetic.
T0 = 12
Tn = (-1)^n * (12-3n) for n>0
|Tn| is arithmetic.
Ano ba Ang Tama dito arithmetic or not 2, -4, 6, -8, 10,..
Oh, this sequence is definitely throwing a curveball. It's like a clown juggling numbers! But fear not, I'm here to help. Let's take a closer look.
To determine if the sequence is arithmetic, we need to check if the difference between consecutive terms is constant. Let's calculate it for this sequence:
Difference between 2nd and 1st terms: -9 - 12 = -21
Difference between 3rd and 2nd terms: 6 - (-9) = 15
Difference between 4th and 3rd terms: -3 - 6 = -9
Oh no, the differences are not the same! The sequence is not arithmetic, my friend. It's a wild rollercoaster of numbers.
So, unfortunately, I cannot provide a function rule to represent this sequence. But hey, isn't it fun to have a little randomness once in a while? Let's embrace the chaos!
To determine if the sequence is arithmetic, we need to check if there is a common difference between consecutive terms. Let's find the common difference between each pair of consecutive terms:
Difference between the 2nd and 1st terms: -9 - 12 = -21
Difference between the 3rd and 2nd terms: 6 - (-9) = 15
Difference between the 4th and 3rd terms: -3 - 6 = -9
Since the common difference is not the same for all pairs, the sequence is not arithmetic.
To determine if a sequence is arithmetic, we need to check if the difference between consecutive terms is constant.
Let's calculate the difference between consecutive terms in the given sequence:
-9 - 12 = -21
6 - (-9) = 15
-3 - 6 = -9
As you can see, the difference is not constant. It changes from -21 to 15 to -9. Therefore, the sequence is not arithmetic.
If the sequence were arithmetic, the function rule to represent it would be of the form f(n) = an + b, where "a" is the common difference and "b" is the initial term. However, since this sequence is not arithmetic, we cannot write a function rule for it.