Question

SThe sixth term of an arithmetic sequence is35and the twelfth term is2What is the common difference of the arithmeticsequence?The common difference isDONE

Answer 1

Given:

The sixth term of an arithmetic sequence is

`a_6=(3)/(2)`

The twelfth term is

`a_(20)=(5)/(2)`

To find:

The common difference

Step-by-step explanation:

The nth term formula of an arithmetic sequence is,

`a_n=a+(n-1)d`

So, the sixth and twelfth terms become,

`\begin{gathered} a_6=a+(6-1)d \\ (3)/(2)=a+5d..............(1) \\ a_(20)=a+(12-1)d \\ (5)/(2)=a+11d.............(2) \end{gathered}`

Subtract (1) from (2),

`\begin{gathered} (5)/(2)-(3)/(2)=11d-5d \\ (2)/(2)=6d \\ 6d=1 \\ d=(1)/(6) \end{gathered}`

Thus, the common difference is,

`d=(1)/(6)`

Final answer:

The common difference is,

`d=(1)/(6)`