The nth term of this number sequence
2, 4, 6, 8,..

nth term is 2n.

Step-by-step explanation:

Hi! To find nth term of this sequence, we must determine whether if this sequence is arithmetic or geometric.

If it’s arithmetic, it has a common difference.

If it’s geometric, it has a common ratio.

According to the sequence, it is arithmetic sequence because it has common difference.

4-2 = 2

6-4 = 2

8-6 = 2

If we keep subtracting next term with previous term, we’ll get 2. Hence, 2 is our common difference.

Now, we know that this sequence is arithmetic. To find nth term or rather say general term, we can use the formula below.

Arithmetic General Term

Where a_n stands for nth term, a_1 is first term and d is common difference.

We know that our first term is 2 and our common difference is 2.

Hence, the nth term is 2n. Also this sequence is basically an even number sequence and all even numbers are multiple of 2.

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!