find a formula for the nth term in this arithmetic sequence: a1 = -7, a2 = -1, a3 = 5, a4 = 11, ... an = ?n +
find a formula for the nth term in this arithmetic sequence: a1 = -7, a2 = -1, a3 = 5, a4 = 11, ... an = ?n +
Answer
Explanation:
Step1: Find the common difference
The common difference $d$ of an arithmetic sequence is found by subtracting consecutive terms. $d=a_{2}-a_{1}=-1 - (-7)=6$.
Step2: Use the formula for the nth - term of an arithmetic sequence
The formula for the nth - term of an arithmetic sequence is $a_{n}=a_{1}+(n - 1)d$. Here, $a_{1}=-7$ and $d = 6$. Expand the formula: $a_{n}=-7+(n - 1)\times6=-7 + 6n-6=6n-13$.
Answer:
$a_{n}=6n - 13$