Find the type of the progression¶
Find the type of the progression (arithmetic progression/geometric progression)
and the next successive member of a given three successive members of a sequence.
According to Wikipedia, an arithmetic progression (AP) is a sequence of numbers
such that the difference of any two successive members of the sequence
is a constant. For instance, the sequence 3, 5, 7, 9, 11, 13, … is an
arithmetic progression with common difference 2. For this problem, we will
limit ourselves to arithmetic progression whose common difference is a
non-zero integer.
On the other hand, a geometric progression (GP) is a sequence of numbers where
each term after the first is found by multiplying the previous one by a fixed
non-zero number called the common ratio. For example, the sequence
2, 6, 18, 54, … is a geometric progression with common ratio 3.
For this problem, we will limit ourselves to geometric progression whose common
ratio is a non-zero integer.
def ap_gp_sequence(arr):
if arr[0]==arr[1]==arr[2]==0:
return "Wrong Numbers"
else:
if arr[1] - arr[0] == arr[2] - arr[1]:
n = 2*arr[2] - arr[1]
return "AP sequence, "+'Next number of the sequence: ' + str(n)
else:
n = arr[2]**2/arr[1]
return "GP sequence, " + 'Next number of the sequence: ' + str(n)
print(ap_gp_sequence([1,2,3]))
print(ap_gp_sequence([2,6,18]))
print(ap_gp_sequence([0,0,0]))
Output:
AP sequence, Next number of the sequence: 4
GP sequence, Next number of the sequence: 54.0
Wrong Numbers