Sum of elements of a Geometric Progression (GP) in a given range

Given a Geometric Progression series in arr[] and Q queries in the form of [L, R], where L is the left boundary of the range and R is the right boundary. The task is to find the sum of the Geometric Progression elements in the given range.

Note: The range is 1-indexed and1 ≤ L, R ≤ N, where N is the size of arr.
Examples: 

Input: arr[] = {2, 4, 8, 16, 32, 64, 128, 256}, Q = [[2, 4], [2, 6], [5, 8]] 
Output: 
28 
124 
480
Explanation: 
Range 1: arr = {4, 8, 16}. Therefore sum = 28 
Range 2: arr = {4, 8, 16, 32, 64}. Therefore sum = 124 
Range 3: arr = {32, 64, 128, 256}. Therefore sum = 480

Input: arr[] = {7, 7, 7, 7, 7, 7}, Q = [[1, 6], [2, 4], [3, 3]] 
Output: 
42
21 

Explanation: 
Range 1: arr = {7, 7, 7, 7, 7, 7}. Therefore sum = 42
Range 2: arr = {7, 7, 7}. Therefore sum = 21 
Range 3: arr = {7}. Therefore sum = 7

Approach: Since the given sequence is an Geometric progression, the sum can be easily found out in two steps efficiently:



  1. Get the first element of the range.
  2. If d = 1, then multiply d*k to it, else multiply the (dk – 1)/(d – 1) to it, where d is the common ratio of the GP and k is number of elements in the range.

For example: 
Suppose a[i] be the first element of the range, d be the common ratio of GP and k be the number of elements in the given range. 
Then the sum of the range would be 

= a[i] + a[i+1] + a[i+2] + ….. + a[i+k-1] 
= a[i] + (a[i] * d) + (a[i] * d * d) + …. + (a[i] *  dk) 
= a[i] *  (1 + d + … + dk
= a[i] * (dk – 1)/(d – 1)

Below is the implementation of the above approach: 

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ program to find the sum 
// of elements of an GP in the 
// given range
#include <bits/stdc++.h>
using namespace std;
  
// Function to find sum in the given range 
int findSum(int arr[], int n, 
            int left, int right) 
      
    // Find the value of k 
    int k = right - left + 1; 
  
    // Find the common difference 
    int d = arr[1] / arr[0]; 
  
    // Find the sum 
    int ans = arr[left - 1]; 
      
    if (d == 1) 
        ans = ans * d * k; 
    else
        ans = ans * ((int)pow(d, k) - 1 / 
                                 (d - 1)); 
          
    return ans; 
  
// Driver Code
int main()
{
    int arr[] = { 2, 4, 8, 16, 32, 
                  64, 128, 256 }; 
    int queries = 3; 
    int q[][2] = { { 2, 4 }, { 2, 6 },
                   { 5, 8 } }; 
      
    int n = sizeof(arr) / sizeof(arr[0]); 
      
    for(int i = 0; i < queries; i++) 
        cout << (findSum(arr, n, q[i][0], q[i][1]))
             << endl; 
  
    return 0;
}
  
// This code is contributed by divyeshrabadiya07

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to find the sum 
// of elements of an GP in the 
// given range 
import java.io.*; 
import java.util.*; 
  
class GFG{ 
      
// Function to find sum in the given range 
static int findSum(int[] arr, int n, 
                int left, int right) 
      
    // Find the value of k 
    int k = right - left + 1
  
    // Find the common difference 
    int d = arr[1] / arr[0]; 
  
    // Find the sum 
    int ans = arr[left - 1]; 
      
    if (d == 1
        ans = ans * d * k; 
    else
        ans = ans * ((int)Math.pow(d, k) - 1
                                (d - 1)); 
          
    return ans; 
  
// Driver Code 
public static void main(String args[]) 
    int[] arr = { 2, 4, 8, 16, 32
                64, 128, 256 }; 
    int queries = 3
    int[][] q = { { 2, 4 }, { 2, 6 }, { 5, 8 } }; 
      
    int n = arr.length; 
      
    for(int i = 0; i < queries; i++) 
        System.out.println(findSum(arr, n, q[i][0], 
                                        q[i][1])); 
  
// This code is contributed by offbeat 

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 program to 
# find the sum of elements 
# of an GP in the given range 
  
# Function to find sum in the given range 
def findSum(arr, n, left, right): 
  
    # Find the value of k 
    k = right - left + 1
  
    # Find the common difference 
    d = arr[1] // arr[0
  
    # Find the sum 
    ans = arr[left - 1
    if d == 1
        ans = ans * d *
    else
        ans = ans * (d ** k - 1) // (d -1
    return ans 
  
# Driver code 
if __name__ == '__main__'
    arr = [ 2, 4, 8, 16, 32, 64, 128, 256
    queries = 3
    q = [[ 2, 4 ], [ 2, 6 ], [ 5, 8 ]] 
    n = len(arr) 
  
    for i in range(queries): 
        print(findSum(arr, n, q[i][0], q[i][1])) 

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to find the sum
// of elements of an GP in the 
// given range 
using System; 
  
class GFG{
      
// Function to find sum in the given range 
static int findSum(int[] arr, int n,
                   int left, int right)
{
      
    // Find the value of k 
    int k = right - left + 1;
  
    // Find the common difference 
    int d = arr[1] / arr[0];
  
    // Find the sum 
    int ans = arr[left - 1];
      
    if (d == 1) 
        ans = ans * d * k;
    else
        ans = ans * ((int)Math.Pow(d, k) - 1 / 
                                      (d - 1)); 
          
    return ans;
}
  
// Driver Code 
public static void Main(string []args) 
    int[] arr = { 2, 4, 8, 16, 32,
                  64, 128, 256 };
                    
    int queries = 3;
    int[,] q = { { 2, 4 }, { 2, 6 }, { 5, 8 } }; 
      
    int n = arr.Length;
      
    for(int i = 0; i < queries; i++)
        Console.Write(findSum(arr, n, q[i, 0], 
                                      q[i, 1]) + "\n");
  
// This code is contributed by rutvik_56

chevron_right


Output: 

28
124
480

  • Time complexity: O(Q) 
  • Space complexity: O(1)

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.




My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.