the first four terms of an arithmetic sequence are -11, -5, 1, 7. what is the equation for $a_n$?\na…

the first four terms of an arithmetic sequence are -11, -5, 1, 7. what is the equation for $a_n$?\na $a_n=-11(n - 1)-6$\nb $a_n=6(n - 1)-11$\nc $a_n=-11(n - 1)+6$\nd $a_n=-6(n - 1)-11$

the first four terms of an arithmetic sequence are -11, -5, 1, 7. what is the equation for $a_n$?\na $a_n=-11(n - 1)-6$\nb $a_n=6(n - 1)-11$\nc $a_n=-11(n - 1)+6$\nd $a_n=-6(n - 1)-11$

Answer

Explanation:

Step1: Find the common - difference

The common - difference $d$ of an arithmetic sequence is found by subtracting the first term from the second term. Given $a_1=-11$ and $a_2 = - 5$, then $d=a_2 - a_1=-5-(-11)=6$.

Step2: Recall the formula for the $n$th term of an arithmetic sequence

The formula for the $n$th term of an arithmetic sequence is $a_n=a_1+(n - 1)d$, where $a_1$ is the first term and $d$ is the common - difference.

Step3: Substitute the values of $a_1$ and $d$ into the formula

Here, $a_1=-11$ and $d = 6$. Substituting these values into the formula $a_n=a_1+(n - 1)d$, we get $a_n=-11+(n - 1)\times6=6(n - 1)-11$.

Answer:

B. $a_n = 6(n - 1)-11$