Question

in an arithmetic sequence, the first term, $a_1$, is equal to 5, and the fourth term, $a_4$, is equal to 14. which number represents the common difference of the arithmetic sequence?
answer
$d=1$
$d=2$
$d=3$
$d=4$
submit answer

Explanation:

Step1: Recall arithmetic sequence formula

The nth term of an arithmetic sequence is given by $a_n = a_1 + (n-1)d$, where $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference.

Step2: Substitute known values

We know $a_1=5$, $a_4=14$, and $n=4$. Substitute into the formula:
$14 = 5 + (4-1)d$

Step3: Simplify and solve for d

Simplify the equation:
$14 = 5 + 3d$
Subtract 5 from both sides:
$14 - 5 = 3d$
$9 = 3d$
Divide both sides by 3:
$d = \frac{9}{3} = 3$

Answer:

d = 3