Find the nth term of the sequence 2, 4, 6, 8, 10,…….

To find the nth term of the sequence 2, 4, 6, 8, 10, and so on, we first need to identify the pattern in the numbers. This sequence consists of even numbers starting from 2 and increasing by 2 each time. Let's break it down step by step.

Identifying the Pattern

The sequence can be observed as follows:

• 1st term: 2
• 2nd term: 4
• 3rd term: 6
• 4th term: 8
• 5th term: 10

Each term increases by 2 from the previous term. This consistent difference indicates that the sequence is arithmetic.

General Formula for the nth Term

In an arithmetic sequence, the nth term can be calculated using the formula:

T(n) = a + (n - 1) * d

Where:

• T(n) is the nth term.
• a is the first term of the sequence.
• d is the common difference between the terms.
• n is the term number.

Applying the Formula

For our sequence:

• The first term a is 2.
• The common difference d is 2.

Substituting these values into the formula gives us:

T(n) = 2 + (n - 1) * 2

Now, simplifying this expression:

T(n) = 2 + 2n - 2

T(n) = 2n

Final Result

The nth term of the sequence is given by the formula T(n) = 2n. This means that if you want to find, say, the 5th term, you would calculate:

T(5) = 2 * 5 = 10

Thus, the 5th term is indeed 10, confirming our formula is correct. You can use this formula to find any term in the sequence simply by substituting the value of n.