A Geometric series is a series with a constant ratio between successive terms. The first term of the series is denoted by a and common ratio is denoted by r. The series looks like this :- a, ar, ar2, ar3, ar4, . . .. The task is to find the sum of such a series.
Examples :
Input : a = 1 r = 0.5 n = 10 Output : 1.99805 Input : a = 2 r = 2 n = 15 Output : 65534
A Simple solution to calculate the sum of geometric series.
C++
// A naive solution for calculating sum of // geometric series. #include<bits/stdc++.h> using namespace std; // function to calculate sum of // geometric series float sumOfGP( float a, float r, int n) { float sum = 0; for ( int i = 0; i < n; i++) { sum = sum + a; a = a * r; } return sum; } // driver function int main() { int a = 1; // first term float r = 0.5; // common ratio int n = 10; // number of terms cout << sumOfGP(a, r, n) << endl; return 0; } |
Java
// A naive solution for calculating sum of // geometric series. import java.io.*; class GFG{ // function to calculate sum of // geometric series static float sumOfGP( float a, float r, int n) { float sum = 0 ; for ( int i = 0 ; i < n; i++) { sum = sum + a; a = a * r; } return sum; } // driver function public static void main(String args[]) { int a = 1 ; // first term float r = ( float )( 1 / 2.0 ) ; // common ratio int n = 10 ; // number of terms System.out.printf( "%.5f" ,(sumOfGP(a, r, n))); } } //This code is contributed by Nikita Tiwari |
Python
# A naive solution for calculating sum of # geometric series. # function to calculate sum of # geometric series def sumOfGP(a, r, n) : sum = 0 i = 0 while i < n : sum = sum + a a = a * r i = i + 1 return sum #driver function a = 1 # first term r = ( float )( 1 / 2.0 ) # common ratio n = 10 # number of terms print ( "%.5f" % sumOfGP(a, r, n)), # This code is contributed by Nikita Tiwari |
C#
// A naive solution for calculating // sum of geometric series. using System; class GFG { // function to calculate // sum of geometric series static float sumOfGP( float a, float r, int n) { float sum = 0; for ( int i = 0; i < n; i++) { sum = sum + a; a = a * r; } return sum; } // Driver Code static public void Main () { // first term int a = 1; // common ratio float r = ( float )(1/2.0) ; // number of terms int n = 10 ; Console.WriteLine((sumOfGP(a, r, n))); } } // This code is contributed by Ajit. |
PHP
<?php // A naive solution for calculating // sum of geometric series. // function to calculate sum // of geometric series function sumOfGP( $a , $r , $n ) { $sum = 0; for ( $i = 0; $i < $n ; $i ++) { $sum = $sum + $a ; $a = $a * $r ; } return $sum ; } // Driver Code // first term $a = 1; // common ratio $r = 0.5; // number of terms $n = 10; echo (sumOfGP( $a , $r , $n )); // This code is contributed by Ajit. ?> |
Output :
1.99805
Time Complexity: O(n).
An Efficient solution to solve the sum of geometric series where first term is a and common ration is r
is by the formula :-
sum of series = a(1 – rn)/(1 – r).
Where r = T2/T1 = T3/T2 = T4/T3 . . .
and T1, T2, T3, T4 . . . ,Tn are the first, second, third, . . . ,nth terms respectively.
For example – The series is 2, 4, 8, 16, 32, 64, . . . upto 15 elements. In the above series, find the sum of first 15 elements where
first term a = 2 and common ration r = 4/2 = 2 or = 8/4 = 2
Then,
sum = 2 * (1 – 215) / (1 – 2).
sum = 65534
C++
// An Efficient solution to solve sum of // geometric series. #include<bits/stdc++.h> using namespace std; // function to calculate sum of // geometric series float sumOfGP( float a, float r, int n) { // calculating and storing sum return (a * (1 - pow (r, n))) / (1 - r); } // driver code int main() { float a = 2; // first term float r = 2; // common ratio int n = 15; // number of terms cout << sumOfGP(a, r, n); return 0; } |
Java
// An Efficient solution to solve sum of // geometric series. import java.math.*; class GFG{ // function to calculate sum of // geometric series static float sumOfGP( float a, float r, int n) { // calculating and storing sum return (a * ( 1 - ( int )(Math.pow(r, n)))) / ( 1 - r); } // driver code public static void main(String args[]) { float a = 2 ; // first term float r = 2 ; // common ratio int n = 15 ; // number of terms System.out.println(( int )(sumOfGP(a, r, n))); } } //This code is contributed by Nikita Tiwari. |
Python
# An Efficient solution to solve sum of # geometric series. # function to calculate sum of # geometric series def sumOfGP( a, r, n) : # calculating and storing sum return (a * ( 1 - pow (r, n))) / ( 1 - r) # driver code a = 2 # first term r = 2 # common ratio n = 15 # number of terms print sumOfGP(a, r, n) # This code is contributed by Nikita Tiwari. |
C#
// C# program to An Efficient solution // to solve sum of geometric series. using System; class GFG { // function to calculate sum of // geometric series static float sumOfGP( float a, float r, int n) { // calculating and storing sum return (a * (1 - ( int )(Math.Pow(r, n)))) / (1 - r); } // Driver Code public static void Main() { float a = 2; // first term float r = 2; // common ratio int n = 15; // number of terms Console.Write(( int )(sumOfGP(a, r, n))); } } // This code is contributed by Nitin Mittal. |
PHP
<?php // An Efficient solution to solve // sum of geometric series. // function to calculate sum // of geometric series function sumOfGP( $a , $r , $n ) { // calculating and storing sum return ( $a * (1 - pow( $r , $n ))) / (1 - $r ); } // Driver Code // first term $a = 2; // common ratio $r = 2; // number of terms $n = 15; echo (sumOfGP( $a , $r , $n )); // This code is contributed by Ajit. ?> |
Output :
65534
Time Complexity: Depends on implementation of pow() function in C/C++. In general, we can compute integer powers in O(Log n) time.
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