Determine weather each sequence is arithmetic, geometric,or neither.
1,-5,-11,-17
- 5 - 1 = - 6
- 11 - ( - 5 ) = - 11 + 5 = - 6
-17 - ( - 11 ) = - 17 +11 = - 6
Arithmetic sequence with common difference d = - 6
To determine whether each sequence is arithmetic, geometric, or neither, we need to analyze the differences between terms.
1st term: 1
2nd term: -5
3rd term: -11
4th term: -17
To check if the sequence is arithmetic, we compare the differences between consecutive terms.
Difference between the 1st and 2nd term: -5 - 1 = -6
Difference between the 2nd and 3rd term: -11 - (-5) = -6
Difference between the 3rd and 4th term: -17 - (-11) = -6
Since the differences between consecutive terms are constant (-6), the sequence is arithmetic.
Therefore, the given sequence 1, -5, -11, -17 is ARITHMETIC.
To determine whether a sequence is arithmetic, geometric, or neither, we need to analyze the differences (for an arithmetic sequence) or ratios (for a geometric sequence) between the terms of the sequence.
Let's start by finding the differences between adjacent terms in the sequence:
-5 - 1 = -6
-11 - (-5) = -6
-17 - (-11) = -6
We can see that the differences between the terms (-6) are consistent. This means that the sequence has a common difference, indicating that it is an arithmetic sequence.
To confirm this, we can find the common difference by subtracting any two consecutive terms:
-5 - 1 = -6 (common difference)
So the sequence 1, -5, -11, -17 is an arithmetic sequence with a common difference of -6.