Answer :
Answer:
The sequence is arithmetic progression and the common difference is -5
Step-by-step explanation:
AP = a + (n -1)d
a = first number = 15
d = common difference
Using the second term
10 = 15 + (2-1) d
10 = 15 + (1)d
10 = 15 + d
10-15 = d
d = -5
Using the third term
5 = 15 + (3-1) d
5 = 15 + (2)d
5 = 15 + 2d
5-15 = 2d
-10 = 2d
-10/2 = d
-5 = d
For the Geometric Progression,
GP = ar^n-1
a = first number
r = common ratio
Using the second number of the series
10 = 15 × r^2-1
10/15 = r^1
-2/3 = r
Using the second number of the series
5 = 15 × r^3-1
5/15 = r^2
-1/3 = r^2
r = square root of -1/3
Conclusion: From the above calculations, the arithmetic progression has a constant common difference of -5, and the geometric progression does not have a constant common ratio. Hence, the sequence is an arithmetic one