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 the common difference \( d \)

The common difference \( d \) in an arithmetic sequence is \( a_{n + 1}-a_{n} \). Using \( a_1 = 7 \) and \( a_2 = 4 \), we get \( d=a_2 - a_1=4 - 7=- 3 \).

Step2: Recall the formula for the nth term of an arithmetic sequence

The formula for the nth term of an arithmetic sequence is \( a_n=a_1+(n - 1)d \). Substitute \( a_1 = 7 \) and \( d=-3 \):
\[

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

\]

Answer:

\( a_n=-3n + 10 \), so the first box is \(-3\) and the second box is \(10\)