Question

# Find the nth term of the sequence 2,4,6,8,10,â€¦â€¦.

Hint: Identify the pattern the subsequent terms are following and then find its general term.

According to the question, the given sequence is 2,4,6,8,10,â€¦â€¦
If we observe them carefully, the terms are the nth positive even number from start.
2 is the first positive even number, 4 is the second positive even number, 6 is the third positive even number and so on.
We know that, nth positive even number can be written as $2n$. So, the general term of the given series is:
$\Rightarrow {T_n} = 2n$
Hence, the nth term of the sequence is $2n$.
Note: The sequence is also in arithmetic progression. So, we have
First term, $a = 2$ and common difference, $d = 2$.
We know that the nth term of an A.P. is:
${T_n} = a + \left( {n - 1} \right)d$
Using this formula, the nth term of the given sequence is:
$\Rightarrow {T_n} = 2 + \left( {n - 1} \right) \times 2, \\ \Rightarrow {T_n} = 2 + 2n - 2, \\ \Rightarrow {T_n} = 2n \\$
Here, we have used a different approach but the end result is the same.