# 11.5.6. Geometric Series

If the sum of the first terms of a geometric sequence is given by , find the sequence.

- A
- B
- C
- D

Find the geometric sequence whose first term and last term , given that the sum of its terms .

- A
- B
- C
- D

If the sum of the first terms of a geometric sequence is given by the rule , find its seventh term.

Show SolutionAn equilateral triangle has a side length of cm, where another triangle is drawn inside of it by connecting the midpoints of its sides. If more interior triangles are to be repeatedly drawn the same way as shown in the figure, determine the sum of perimeters of the first drawn 6 triangles to the nearest integer.

- Acm
- Bcm
- Ccm
- Dcm

In a bacterial culture, each bacterium replicates daily. What is the bacterial count in the culture after six days if they were 810 bacteria on the first day?

- A25 110bacteria
- B52 650bacteria
- C102 870bacteria
- D51 030bacteria

Find the sum of the geometric series .

- A13
- B
- CThe series is divergent and has no sum
- D

Given that the sum of an infinite geometric sequence is 52,and its first term is 14, determine its common ratio.

- A
- B
- C
- D

Determine the first term of the infinite geometric sequence whose common ratio is and sum is .

- A
- B
- C
- D