Question

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

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

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 $2n$.
First term, $a = 2$ and common difference, $d = 2$.
${T_n} = a + \left( {n - 1} \right)d$
$\Rightarrow {T_n} = 2 + \left( {n - 1} \right) \times 2, \\ \Rightarrow {T_n} = 2 + 2n - 2, \\ \Rightarrow {T_n} = 2n \\$