Identify the Sequence -1/3 , 1/6 , -1/12

Problem

−1/3,1/6,−1/12,…

Solution

1. Identify the terms of the sequence as (a_1)=−1/3 (a_2)=1/6 and (a_3)=−1/12

2. Calculate the ratio between consecutive terms to check if the sequence is geometric.

3. Divide the second term by the first term:

(a_2)/(a_1)=(1/6)/(−1/3)

(a_2)/(a_1)=1/6⋅(−3/1)=−1/2

4. Divide the third term by the second term:

(a_3)/(a_2)=(−1/12)/(1/6)

(a_3)/(a_2)=−1/12⋅6/1=−1/2

5. Conclude that since there is a constant common ratio r=−1/2 the sequence is a geometric sequence.

Final Answer

Geometric Sequence with *(a_1)=−1/3* and *r=−1/2

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