Question

(Please Help!) The formula to find a certain number in an arithmetic sequence is an=a1+d(n−1) where an represents the nth term of the sequence, a1 is the first term of the sequence, and d is the common difference. Solve for d.

Answer 1

Answer:

The correct option is A) $d=\frac{a_n-a_1}{n-1}$

Step-by-step explanation:

Consider the provide equation.

$a_n=a_1+d(n-1)$

We need to solve the equation for d.

Subtract $a_1$ from both sides

$a_n-a_1=a_1-a_1+d(n-1)$

$a_n-a_1=d(n-1)$

Divide both sides by n-1.

$\frac{a_n-a_1}{n-1}=\frac{d(n-1)}{n-1}$

$d=\frac{a_n-a_1}{n-1}$

Hence, the correct option is A) $d=\frac{a_n-a_1}{n-1}$

Answer 2

Answer:

A

Step-by-step explanation:

you move the a^1 to the left which becomes a^n-a^1. then you move (n-1) to the left as well which becomes a^n-a^1/n-1=d. you switch the places and tada, the answer.