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19 votes
19 votes
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?

User Doug Kaye
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1 Answer

11 votes
11 votes

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.

User Bedna
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