Question

find a formula for the nth term in this arithmetic sequence:
a₁ = 8, a₂ = 4, a₃ = 0, a₄ = -4, ...
aₙ = ?n +

Explanation:

Step1: Find common difference $d$

$d = a_2 - a_1 = 4 - 8 = -4$

Step2: Recall arithmetic sequence formula

The general form of an arithmetic sequence is $a_n = dn + c$, where $c = a_1 - d$.

Step3: Calculate constant term $c$

$c = 8 - (-4) = 8 + 4 = 12$

Step4: Substitute $d$ and $c$

$a_n = -4n + 12$

Answer:

$a_n = -4n + 12$