# Python: Find the type of the progression and the next successive member of a given three successive members of a sequence

## Python Basic - 1: Exercise-27 with Solution

Write a Python program to 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.

**Sample Solution**:

**Python Code:**

```
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]))
```

Sample Output:

AP sequence, Next number of the sequence: 4 GP sequence, Next number of the sequence: 54.0 Wrong Numbers

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**Previous:** Write a Python program to compute the summation of the absolute difference of all distinct pairs in an given array (non-decreasing order).

**Next:** Write a Python program to print the length of the series and the series from the given 3rd term , 3rd last term and the sum of a series.

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