Question

Write an explicit formula for ay, the nth term of the sequence 39, 33, 27, ....

Answer 1

ay = 39 -6(n -1)

Explanation:

The explicit formula for an arithmetic sequence can be written by using the first-term value and the common difference in the generic formula.

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The generic formula for the n-th term of an arithmetic sequence is ...

`a_n=a_1+d(n-1)`

where a₁ is the first term of the sequence (39), and d is the difference between sequential terms (33-39 = -6).

Using the values for this sequence in the generic formula, we have ...

ay = 39 -6(n -1)