What is the Missing Number in the Sequence 2, 4, 6, 8, __, 12, 14?

The missing number in the sequence 2, 4, 6, 8, __, 12, 14 is 10. This sequence represents the multiples of 2, starting from 2 and increasing by 2 each time.

Solving the Sequence

Let's break down the sequence to understand its pattern more clearly:

1. Multiples of 2

This sequence can be identified as a sequence of even numbers. The pattern is straightforward: every number is a multiple of 2. The next number in the sequence is found by adding 2 to the previous number:

2 (2 × 1)4 (2 × 2)6 (2 × 3)8 (2 × 4)10 (2 × 5) - This is the missing number in the sequence12 (2 × 6)14 (2 × 7)

2. Geometric Progression

The sequence can also be viewed as a geometric progression where each term is a multiple of 2. Here's the sequence explained in terms of this progression:

2 × 1 22 × 2 42 × 3 62 × 4 82 × 5 10 - The missing number2 × 6 122 × 7 14

3. General Formula

We can use a general formula to find the nth term in the sequence:

an 2 × n

Using this formula, we find that the 5th term (n5) is:

a5 2 × 5 10

Conclusion

In sum, the missing number in the sequence 2, 4, 6, 8, __, 12, 14 is 10. This sequence is a simple yet illustrative example of a pattern involving multiples of 2. Understanding patterns and sequences is essential in mathematics and problem-solving.

Code Implementation

Here's a simple C code snippet that generates the sequence using a for loop:

#include iostreamusing namespace std;int main() {    int i;    for(i1; i10; i  ) {        int n  2 * i;        cout  n  " ";    }    return 0;}

When you run this code, it outputs:

2 4 6 8 10 12 14 16 18 20 

This output confirms the correct sequence and the missing number 10.