What is the sum of the geometric series

Hence, the sum of the geometric series is:

                                      259

Step-by-step explanation:

We are given a geometric series as:

i.e. we are asked to fnd the sum of first four terms of the geometric series with first term as 1

Since, the series is:

Also, the common ratio of the series is: r=6

Since, each of the term of the series is 6 times it's preceding term.

Also we know that sum of a finite geometric series with n-terms and common ratio r is calculated by the formula:

Here we have: a=1 and r=6 and n=4

Hence,

                        Hence, the sum of the series is:

                                     259

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

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