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

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=\frac32` and
`a_(12)=\frac52`, so we get


`\frac52=\frac32+6d\implies 6d=1\implies d=\frac16`

Answer 2

The Next one is C

Explanation: