Question

an arithmetic sequence has first term 2 and second term 4. what is the third term?
the third term is a.

Explanation:

Step1: Find the common difference

The common difference $d$ of an arithmetic - sequence is given by $d=a_{2}-a_{1}$. Here, $a_{1} = 2$ and $a_{2}=4$, so $d = 4 - 2=2$.

Step2: Calculate the third term

The $n$th term of an arithmetic sequence is $a_{n}=a_{1}+(n - 1)d$. For the third term ($n = 3$), $a_{3}=a_{1}+2d$. Substitute $a_{1}=2$ and $d = 2$ into the formula: $a_{3}=2+2\times2$.
$a_{3}=2 + 4=6$.

Answer:

6