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

$a_6=\frac{3}{2}$

The twelfth term is

$a_{20}=\frac{5}{2}$

To find:

The common difference

Explanation:

The nth term formula of an arithmetic sequence is,

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

So, the sixth and twelfth terms become,

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

Subtract (1) from (2),

$\begin{gathered} \frac{5}{2}-\frac{3}{2}=11d-5d \\ \frac{2}{2}=6d \\ 6d=1 \\ d=\frac{1}{6} \end{gathered}$

Thus, the common difference is,

$d=\frac{1}{6}$

Final answer:

The common difference is,

$d=\frac{1}{6}$