Question 1:   In the geometric series $\left(a_n\right)$ it’s known that $a_{10}=2$ . Find product of the nineteen first terms of this progression.

Question 2:   The second term of the geometric series is $a_2=4$ . Find the product of three first terms of this progression.

Question 3:   Find the initial term and the common ratio of a geometric series $\left(a_n\right)$ , if $a_5=3a_3;a_6-a_2=48$ .

Question 4:   Find the initial term and the common ratio of a geometric sequence which consists of $6$ terms. The sum of the first three terms is $168$ , the sum of the last three terms is $21$ .

Question 5:   The sum of three positive sequent numbers that make up an arithmetic series $\left(a_n\right)$ is $21$ . If you add $2, 3, 9$ to these numbers, they would make up a geometric series $\left(b_n\right)$ . Find these initial numbers.

Question 6:   The sum of three sequent numbers that make up a geometric series $\left(b_n\right)$ is $65$ . If you subtract $1$ from the first one and $19$ from the second one, you get an arithmetic series $\left(a_n\right)$ . Find the sequence of these initial numbers.

Question 7:   For any natural $n$ , the sum of the first $n$ terms of a geometric series $\left(b_n\right)$ is given by a formula $S_n=6\left({\left(-\frac{1}{2}\right)}^n-1\right)$ . Find the fourth term of this progression.

Question 8:   Find the sum of squares of six first terms of a geometric series $\left(a_n\right)$ with the first term $a_1=2\sqrt{3}$ and a common ratio $r=\sqrt{3}$ .

Question 9:   Find the sum of cubes of the first four terms of a geometric series $\left(b_n\right)$ if $b_1=3;b_2=-6$ .

Question 10:   Find the sum of the infinite geometric series $\left(a_n\right)$ if $a_2\times a_4=36; a_3+a_5=8$ .