tell whether the sequence is arithmetic. If it is, what is the common difference? -12,-7,-2,3,...
5 added each time.
To determine if the given sequence (-12, -7, -2, 3, ...) is arithmetic and find the common difference, we need to check if there is a constant difference between consecutive terms.
Step 1: Find the difference between consecutive terms.
The difference between the first and second terms is: -7 - (-12) = 5.
The difference between the second and third terms is: -2 - (-7) = 5.
The difference between the third and fourth terms is: 3 - (-2) = 5.
Step 2: Verify if there is a constant difference between the terms.
Since the difference between each consecutive pair of terms is consistently 5, we can conclude that the sequence is arithmetic.
Step 3: Find the common difference.
The common difference, or the constant difference, is calculated as the difference between any two consecutive terms. In this case, the common difference is 5.
Therefore, the given sequence (-12, -7, -2, 3, ...) is arithmetic with a common difference of 5.
To determine whether a sequence is arithmetic, we need to check if there is a common difference between consecutive terms.
In the given sequence: -12, -7, -2, 3, ...
We can calculate the differences between consecutive terms:
-12 - (-7) = -12 + 7 = -5
-7 - (-2) = -7 + 2 = -5
-2 - 3 = -2 - 3 = -5
Since the difference between each pair of consecutive terms is -5, which is a constant value, we can conclude that the sequence is arithmetic.
Additionally, the common difference is -5.