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

Answer

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

Complete step-by-step answer:

According to the question, the given sequence is 2,4,6,8,10,……

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.

Complete step-by-step answer:

According to the question, the given sequence is 2,4,6,8,10,……

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.

Last updated date: 31st May 2023

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