Question

an arithmetic sequence is given below. 8, 12, 16, 20, ... write an explicit formula for the n^th term a_n.

Explanation:

Step1: Identify first term $a_1$

The first term of the sequence is $a_1 = 8$.

Step2: Calculate common difference $d$

Subtract consecutive terms: $d = 12 - 8 = 4$.

Step3: Apply arithmetic sequence formula

The explicit formula for an arithmetic sequence is $a_n = a_1 + (n-1)d$. Substitute $a_1=8$ and $d=4$:

$$\begin{align*} a_n &= 8 + (n-1) \times 4 \\ &= 8 + 4n - 4 \\ &= 4n + 4 \end{align*}$$

Answer:

$a_n = 4n + 4$