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Find the Sum of the series 1, 2, 3, 6, 9, 18, 27, 54, … till N terms
• Last Updated : 18 Mar, 2021

Given a number N, the task is to find the sum of the below series till N terms. Examples:

Input: N = 8
Output: 201
1 + 2 + 3 + 6 + 9 + 18 + 27 + 54 + 81 = 201
Input: N = 12
Output: 1821
1 + 2 + 3 + 6 + 9 + 18 + 27 + 54 + 81 + 162 + 243 + 486 + 729 = 1821

Approach: From the given series, find the formula for Nth term:

```1st term = 1
2nd term = 2 = 2 * 1
3rd term = 3 = 3/2 * 2
4th term = 6 = 2 * 3
5th term = 9 = 3/2 * 6
6th term = 18 = 2 * 9
.
.
Nth term = [2 * (N-1)th term], if N is even
[3/2 * (N-1)th term], if N is odd```

Therefore:

Nth term of the series

```*** QuickLaTeX cannot compile formula:

*** Error message:
Error: Nothing to show, formula is empty
```

Then iterate over numbers in the range [1, N] to find all the terms using the above formula and compute their sum.
Approach: By observing the pattern in the given series, the next numbers of the series are alternatively multiplied by 2 and 3/2.
Below is the implementation of the above approach:

## C++

 `// C++ program for the above series``#include ``using` `namespace` `std;` `// Function to find the sum of series``void` `printSeriesSum(``int` `N)``{``    ``double` `sum = 0;` `    ``int` `a = 1;``    ``int` `cnt = 0;` `    ``// Flag to find the multiplicating``    ``// factor.. i.e, by 2 or 3/2``    ``bool` `flag = ``true``;` `    ``// First term``    ``sum += a;` `    ``while` `(cnt < N) {` `        ``int` `nextElement;` `        ``// If flag is true, multiply by 2``        ``if` `(flag) {``            ``nextElement = a * 2;``            ``sum += nextElement;``            ``flag = !flag;``        ``}` `        ``// If flag is false, multiply by 3/2``        ``else` `{``            ``nextElement = a * 3 / 2;``            ``sum += nextElement;``            ``flag = !flag;``        ``}` `        ``// Update the previous element``        ``// to nextElement``        ``a = nextElement;``        ``cnt++;``    ``}` `    ``// Print the sum``    ``cout << sum << endl;``}` `// Driver Code``int` `main()``{` `    ``int` `N = 8;` `    ``printSeriesSum(N);``    ``return` `0;``}`

## Java

 `// Java program for the above series``class` `GFG {``    ` `    ``// Function to find the sum of series``    ``static` `void` `printSeriesSum(``int` `N)``    ``{``        ``double` `sum = ``0``;``    ` `        ``int` `a = ``1``;``        ``int` `cnt = ``0``;``    ` `        ``// Flag to find the multiplicating``        ``// factor.. i.e, by 2 or 3/2``        ``boolean` `flag = ``true``;``    ` `        ``// First term``        ``sum += a;``    ` `        ``while` `(cnt < N) {``    ` `            ``int` `nextElement;``    ` `            ``// If flag is true, multiply by 2``            ``if` `(flag == ``true``) {``                ``nextElement = a * ``2``;``                ``sum += nextElement;``                ``flag = !flag;``            ``}``    ` `            ``// If flag is false, multiply by 3/2``            ``else` `{``                ``nextElement = a * ``3` `/ ``2``;``                ``sum += nextElement;``                ``flag = !flag;``            ``}``    ` `            ``// Update the previous element``            ``// to nextElement``            ``a = nextElement;``            ``cnt++;``        ``}``    ` `        ``// Print the sum``        ``System.out.println(sum);``    ``}``    ` `    ``// Driver Code``    ``public` `static` `void` `main (String[] args)``    ``{``    ` `        ``int` `N = ``8``;``    ` `        ``printSeriesSum(N);``    ``}``}``// This code is contributed by AnkitRai01`

## Python3

 `# Python3 program for the above series` `# Function to find the sum of series``def` `printSeriesSum(N) :` `    ``sum` `=` `0``;` `    ``a ``=` `1``;``    ``cnt ``=` `0``;` `    ``# Flag to find the multiplicating``    ``# factor.. i.e, by 2 or 3/2``    ``flag ``=` `True``;` `    ``# First term``    ``sum` `+``=` `a;` `    ``while` `(cnt < N) :` `        ``nextElement ``=` `None``;` `        ``# If flag is true, multiply by 2``        ``if` `(flag) :``            ``nextElement ``=` `a ``*` `2``;``            ``sum` `+``=` `nextElement;``            ``flag ``=` `not` `flag;` `        ``# If flag is false, multiply by 3/2``        ``else` `:``            ``nextElement ``=` `a ``*` `(``3` `/` `2``);``            ``sum` `+``=` `nextElement;``            ``flag ``=` `not` `flag;` `        ``# Update the previous element``        ``# to nextElement``        ``a ``=` `nextElement;``        ``cnt ``+``=` `1` `    ``# Print the sum``    ``print``(``sum``);` `# Driver Code``if` `__name__ ``=``=` `"__main__"` `:`  `    ``N ``=` `8``;` `    ``printSeriesSum(N);``    ` `    ``# This code is contributed by AnkitRai01`

## C#

 `// C# program for the above series``using` `System;` `class` `GFG {``    ` `    ``// Function to find the sum of series``    ``static` `void` `printSeriesSum(``int` `N)``    ``{``        ``double` `sum = 0;``    ` `        ``int` `a = 1;``        ``int` `cnt = 0;``    ` `        ``// Flag to find the multiplicating``        ``// factor.. i.e, by 2 or 3/2``        ``bool` `flag = ``true``;``    ` `        ``// First term``        ``sum += a;``    ` `        ``while` `(cnt < N) {``    ` `            ``int` `nextElement;``    ` `            ``// If flag is true, multiply by 2``            ``if` `(flag == ``true``) {``                ``nextElement = a * 2;``                ``sum += nextElement;``                ``flag = !flag;``            ``}``    ` `            ``// If flag is false, multiply by 3/2``            ``else` `{``                ``nextElement = a * 3 / 2;``                ``sum += nextElement;``                ``flag = !flag;``            ``}``    ` `            ``// Update the previous element``            ``// to nextElement``            ``a = nextElement;``            ``cnt++;``        ``}``    ` `        ``// Print the sum``        ``Console.WriteLine(sum);``    ``}``    ` `    ``// Driver Code``    ``public` `static` `void` `Main (``string``[] args)``    ``{``    ` `        ``int` `N = 8;``    ` `        ``printSeriesSum(N);``    ``}``}` `// This code is contributed by AnkitRai01`

## Javascript

 ``
Output:
`201`

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