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Write an explicit formula for a,, the nth term of the sequence 72, -12, 2, ....

1 Answer

13 votes

Answer:


a_n=72 \cdot \left(-\frac16 \right)^(n-1)

Explanation:

The difference between each term in the sequence is not the same, therefore the sequence is a geometric sequence.

Geometric sequence formula:
a_n=a r^(n-1)

where
a is the start term and
r is the common ratio

Given
a_1 = 72 \implies a=72

To calculate
r, divide one term by its previous term:


\implies r=(a_3)/(a_2)=(2)/(-12)=-\frac16

Therefore,
a_n=72 \cdot \left(-\frac16 \right)^(n-1)

User Freonix
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