Answer:
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
[tex]\displaystyle \large{a_n=a_1+(n-1)d}[/tex]
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.
[tex]\displaystyle \large{a_n=2+(n-1)2}\\
\displaystyle \large{a_n=2+2n-2}\\
\displaystyle \large{a_n=2n}[/tex]
Hence, the nth term is 2n. Also this sequence is basically an even number sequence and all even numbers are multiple of 2.
