5,-15,45,-135 is it arithmetic , geometric or neither ?
a = 5
r = -3
an = a r^(n-1)
which is the very definition of a geometric sequence :)
To determine if the sequence 5, -15, 45, -135 is arithmetic, geometric, or neither, we need to analyze the differences or ratios between the terms.
Arithmetic sequence:
An arithmetic sequence is a sequence in which the difference between any two consecutive terms is constant. To check if a sequence is arithmetic, we calculate the differences between consecutive terms.
In this case, let's calculate the differences between consecutive terms:
-15 - 5 = -20
45 - (-15) = 60
-135 - 45 = -180
As we can see, the differences are not constant, meaning the sequence is not arithmetic.
Geometric sequence:
A geometric sequence is a sequence in which each term is found by multiplying the previous term by a constant ratio. To check if a sequence is geometric, we calculate the ratios between consecutive terms.
In this case, let's calculate the ratios between consecutive terms:
-15 ÷ 5 = -3
45 ÷ (-15) = -3
-135 ÷ 45 = -3
As we can see, the ratios between consecutive terms are constant (-3 in this case), which indicates that the sequence is geometric.
Conclusion:
Based on our analysis, we can conclude that the sequence 5, -15, 45, -135 is geometric because the ratios between consecutive terms are constant.