Classify the series as arithmetic or geometric then determine whether the series is convergent or divergent

Geometric , convergent

Step-by-step explanation:

Given sequence is    {  12 + ( -8 )  + 16/3 + ( - 32/9 ) + 64/27 + . . .  . . . . }

To check whether the sequence is arithmetic , we first find difference of first two terms then find difference of third and second term .

If we get both the difference same , then it is arithmetic .

d₁   =   - 8 - ( 12 ) =  - 20

           16                              40

d₂  =       - ( - 8 )  =    

             3                                3

Common difference is not same , thus it is not arithmetic .

To check whether sequence is geometric , we divide second by first term and then third by second term . If we get the same ratio , then it is geometric .

             -8              - 2

r₁   =   =  

             12                3

            16/3           16                     -2

r₂   =   =        =    

            - 8              3 * ( -8)              3

Thus common ratio is same , so it is geometric .

Now we need to check whether it is convergent or divergent .

We have an infinite geometric series .

It is convergent if | r | < 1 , that is common ratio is less than 1 .

We have | r |  = | - 2/3 |  = | - 0.66 |  = 0.66 < 1 .

Thus the  geometric series converges .

Thus given series is geometric , convergent .

Third is the correct option .

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

3030 ur welcome

step-by-step explanation: