Question

The 12th term of an arithmetic sequence is 87 and the 20th term is 135. Which number represents the value of the common difference of the sequence?

Answer 1

Let d be the common difference of the given sequence.

Given that,

`\begin{gathered} a_(12)=87 \\ a_(20)=135 \end{gathered}`

By definition,

`\begin{gathered} a_n=a_1+(n-1)d \\ d=(a_n-a_1)/(n-1) \end{gathered}`

For, n = 12,

`d=(87-a_1)/(11)`

For, n = 20,

`d=(135-a_1)/(19)`

Therefore,

`\begin{gathered} (87-a_1)/(11)=(135-a_1)/(19) \\ 1653-19a_1=1485-11a_1 \\ 8a_1=168 \\ a_1=21 \end{gathered}`

Therefore, common difference,

`\begin{gathered} d=(87-21)/(11) \\ =(66)/(11) \\ =6 \end{gathered}`

Therefore, common difference is 6.