The first three terms of an arithmetic sequence are 3k-1, 4k+1, 6k-2. What is the value of k?

k = 5

Step-by-step explanation:

First three terms of an AP are 3k-1, 4k+1, 6k-2.

First term is 3k-1

For an AP,

a₂-a₁=a₃-a₂

4k+1-(3k-1)=6k-2-(4k+1)

4k+1-3k+1=6k-2-4k-1

k+2=2k-3

Separating like terms,

k-2k=-3-2

-k=-5

k = 5

So, the value of k is 5.

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.