Determine whether the following sequence is arithmetic, geometric, or neither.
1 1/3, 2, 2 2/3, 3 1/3

arith

Step-by-step explanation:

Let's check whether or not this is a geometric series.

The first term is 1 1/3, or 4/3.

What would the common ratio be, to convert this 4/3 into the 2nd term, 2?

(4/3)r = 2, or r = 2(3/4) = 6/4 = 3/2.

Assuming that the common ratio is r = 3/2, will multiplying 2 by 3/2 result in the 3rd term, 2  2/3?  NO.  So this is NOT a geometric progression.

The difference between 1  1/3 and 2 is 2/3.  If we add 2/3 to 2, we get 2  2/3, which agrees with the given 3rd term.  

If we add 2/3 to 2  2/3, do we get the fourth given term, 3  1/3?

2/3 + 2  2/3 is equivalent to 2  4/3, or 10/3, which is equivalent to 3  1/3.

Thus, this IS an arithmetic sequence, and the common difference is 2/3.

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.

35%

step-by-step explanation: