The given sequence is 2, 4, 6, 8, 10. To find the general term of this sequence, it’s essential to identify the pattern within the numbers.

First, observe the numbers: each term increases by a value of 2. This is a clear indication that we are dealing with an arithmetic sequence. In an arithmetic sequence, the common difference (the amount added to each term to get the next) remains constant. Here, the common difference (d) is 2.

To represent the general term of an arithmetic sequence, we use the formula:

 a_n = a_1 + (n - 1)d 

Where:

• a_n is the nth term we are trying to find.
• a_1 is the first term of the sequence.
• n is the term number.
• d is the common difference.

In our case:

• a_1 = 2 (the first term)
• d = 2 (the common difference)

Substituting these values into the formula gives us:

 a_n = 2 + (n - 1) * 2 

Simplifying this, we have:

 a_n = 2 + 2n - 2 

Thus, the equation simplifies to:

 a_n = 2n 

This means that the general term for the sequence 2, 4, 6, 8, 10 is a_n = 2n. So, for any natural number n, you can find the nth term of this sequence by simply multiplying n by 2.

For example:

• If n = 1, a_1 = 2 * 1 = 2
• If n = 2, a_2 = 2 * 2 = 4
• If n = 3, a_3 = 2 * 3 = 6
• If n = 4, a_4 = 2 * 4 = 8
• If n = 5, a_5 = 2 * 5 = 10

Thus, the formula effectively captures the essence of the sequence while allowing anyone to predict future terms with ease!