Tell whether the sequence 1/3, 0, 1, -2 is arithmetic, geometric, or neither. find the next three terms of the sequence.

a. neither; 7, -20, 61
b. geometric; 7, -20, 61
c. arithmetic; -1/3, 1 1/3, 3
d. geometric; -3 1/3, -5 5/9, -9 7/27

A. neither; 7, -20, 61

Step-by-step explanation:

The sequence 1/3, 0, 1, -2 ...

The difference between the terms are; -1/3, 1, -3

Looking the difference between consecutive terms in the sequence, we can predict the next differences between the following terms, as the differences form a geometric sequence;

Therefore; -1/3, 1, -3, 9, -27, 81

Thus; the sequence will be;

1/3, 0, 1, -2 , (-2+9), (-2+9+-27), (-2+9+-27+81)

1/3, 0, 1, -2, 7, -20, 61

Hence the next three terms are; 7, -20, 61

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2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.