**QUESTION**

Given an array that represents elements of geometric progression in order. One element is missing in the progression, find the missing number. It may be assumed that one term is always missing and the missing term is not first or last of series. Take number of elements and the array as input.

“TESTCASE_1”: “4\n2 4 8 32\n###—###SEPERATOR—###—\nThe missing element of Geometric Progression series is 16\n\n”, “TESTCASE_2”: “4\n1 3 27 81\n###—###SEPERATOR—###—\nThe missing element of Geometric Progression series is 9”, “TESTCASE_3”: “4\n4 16 64 1024\n###—###SEPERATOR—###—\nThe missing element of Geometric Progression series is 256”, “TESTCASE_4”: “0\n###—###SEPERATOR—###—\n0”, “TESTCASE_5”: “0\n###—###SEPERATOR—###—\n0

**ANSWER**

```
import java.io.*;
// JAVA Code for Find the missing number
// in Geometric Progression
import java.util.*;
class TestClass {
// It returns INT_MAX in case of error
public static int findMissingRec(int arr[], int low,
int high, int ratio)
{
if (low >= high)
return Integer.MAX_VALUE;
int mid = low + (high - low)/2;
// If element next to mid is missing
if (arr[mid+1]/arr[mid] != ratio)
return (arr[mid] * ratio);
// If element previous to mid is missing
if ((mid > 0) && (arr[mid]/arr[mid-1]) != ratio)
return (arr[mid-1] * ratio);
// If missing element is in right half
if (arr[mid] == arr[0] * (Math.pow(ratio, mid)) )
return findMissingRec(arr, mid+1, high, ratio);
return findMissingRec(arr, low, mid-1, ratio);
}
// Find ration and calls findMissingRec
public static int findMissing(int arr[], int n)
{
// Finding ration assuming that the missing
// term is not first or last term of series.
int ratio =(int) Math.pow(arr[n-1]/arr[0], 1.0/n);
return findMissingRec(arr, 0, n-1, ratio);
}
/* Driver program to test above function */
public static void main(String[] args)
{
Scanner sc=new Scanner(System.in);
int n=sc.nextInt();
int arr[]=new int[n];
for(int i=0;i<n;i++)
arr[i]=sc.nextInt();
System.out.print("The missing element of Geometric Progression series is "+findMissing(arr, n));
}
}
```