Question

The sixth term of an arithmetic sequence is 3/2 , and the twelfth term is 5/2 . What is the common difference of the arithmetic sequence?

Answer 1

The Next one is C

Step-by-step explanation:

Answer 2

Let $a_n$ denote the $n$-th term in the sequence. For an arithmetic sequence, there is a constant number added to successive terms:

$a_7=a_6+d$
$a_8=a_7+d=a_6+2d$
$a_9=a_8+d=a_6+3d$
$\cdots$
$a_{12}=a_{11}+d=a_6+6d$

We know $a_6=\dfrac32$ and $a_{12}=\dfrac52$, so we get

$\dfrac52=\dfrac32+6d\implies 6d=1\implies d=\dfrac16$