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Indicate the general rule for this sequence. Find a1 and the common difference. a4 = 18 a7 = 9

User Pmor
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1 Answer

4 votes

Answer:


a_(n) = 27 - 3(n-1)

Explanation:

Arithmetic sequences concepts:

The general rule of an arithmetic sequence is the following:
a_(n+1) = a_(n) + d

In which d is the common diference between each term.

We can expand the general equation to find the nth term from the first, by the following equation:


a_(n) = a_(1) + (n-1)*d

And also:


a_(n) = a_(m) + (n-m)*d

In this question:


a_(4) = 18, a_(7) = 9

Finding the common ratio:


a_(n) = a_(m) + (n-m)*d


a_(7) = a_(4) + (7-4)*d


9 = 18 + 3d


3d = -9


d = (-9)/(3)


d = -3

Finding the first term:


a_(4) = a_(1) + (4-1)*d


18 = a_(1) + 3*(-3)


a_(1) = 27

General rule:


a_(n) = a_(1) + (n-1)*d


a_(n) = 27 - 3(n-1)

User Ahmed Elbatt
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