Question

find a formula for the nth term in this arithmetic sequence:
a₁ = 7, a₂ = 4, a₃ = 1, a₄ = -2, ...
aₙ = ?n +

Explanation:

Step1: Find common difference $d$

$d = a_2 - a_1 = 4 - 7 = -3$

Step2: Recall arithmetic sequence formula

The general formula for the nth term of an arithmetic sequence is $a_n = a_1 + (n-1)d$.

Step3: Substitute values and simplify

Substitute $a_1=7$ and $d=-3$ into the formula:

$$\begin{align*} a_n &= 7 + (n-1)(-3)\\ &= 7 - 3n + 3\\ &= -3n + 10 \end{align*}$$

Answer:

$a_n = -3n + 10$