Question

nth term of a Sequence Find the nth term of a sequence whose first several terms are given.

$0,2,0,2,0,2,$….

Short answer

The nth term of the sequence is$a_n=\left\{\begin{array}{l}0,n=odd\\ 2,n=even\end{array}\right.$.

Step-by-step solution

Step 1.  Given

The given sequence is 0, 2, 0, 2, 0, 2, …

Step 2.  To determine

We have to find thenth term of the sequence.

Step 3.  Calculation

The given sequence 0, 2, 0, 2, 0, 2…

This is a dual sequence. It has odd positions to be 0 and the even positions to be 2.

So, we can write the sequence as:

$a_n=\left\{\begin{array}{l}0,n=odd\\ 2,n=even\end{array}\right.$

Hence, the nth term of the sequence is$a_n=\left\{\begin{array}{l}0,n=odd\\ 2,n=even\end{array}\right..$