Question

an arithmetic sequence is given below.
-20, -14, -8, -2, ...
write an explicit formula for the ( n^{\text{th}} ) term ( a_n ).

Explanation:

Step1: Identify first term $a_1$

The first term of the sequence is $a_1 = -20$.

Step2: Calculate common difference $d$

Subtract consecutive terms: $d = -14 - (-20) = 6$.

Step3: Apply arithmetic sequence formula

Use the explicit formula for arithmetic sequences: $a_n = a_1 + (n-1)d$.
Substitute $a_1=-20$ and $d=6$:

$$\begin{align*} a_n &= -20 + (n-1) \times 6 \\ &= -20 + 6n - 6 \\ &= 6n - 26 \end{align*}$$

Answer:

$a_n = 6n - 26$