# geometric

1. ### help with geometric distribution exercise

Hello dear forum members. I was requested to answer this exercise that requires the use of geometric distribution. "A bag contains 3 white and 5 black marbles. A marble is extracted with replacement until a black marble is selected. Find the probability that at least k-extractions are required"...
2. ### Two spheres of radii r1 and r2 cut orthogonally. Find radius of common circle.

Find the radius the common circle of intersection and show that it is equal to \frac{r_1 r_2}{\sqrt{r_1^{2} + r_2^{2}}}. When two sphere intersect they form a circle if you join all the points of intersection, that is the common circle. See this image, the silver portion is the common circle...
3. ### Geometric Series Equivalence

Hello, Why is this: Equivalent to this: Thank you.
4. ### Taylor series and Geometric series

To find the taylor series of a function you would usually use the formula $\sum_{n=0}^{\infty}\frac{f^{n}(c)}{n!}(z-c)^n$. However when computing the taylor series for $f(z)=\frac{1}{z+3}$ about $z=1$, I discovered that not only can you compute it using the above formula but you can also...
5. ### Geometric series, find the common ratio.

Given: a=1, 7th term = 4096. formula that we have to use: a_n=ar^n-1 if we plug it in we get: 1=ar^0 4096=ar^6 If we divide the 2nd equation by the first equation all we get is 4096=r^6..... now the answer...
6. ### Geometric distributions.

Question I am struggling on is attached. I can do all the questions bar the last one; apparently, P(X=3) (where X has a geometric distribution) is incorrect. I can't really see why this is as P(X=3) is defined as 'the probability of failing two times and then having a success on the third...
7. ### inverse geometric model arm robot : system equations non linear

Hi, i'm studying a robot arm i have done davenit and direct geometric model and i obtain this equations system eq1=335*cos(t2)* sin(t3) -77*sin(t2)-260*sin(t2)*sin(t4)+260*cos(t2)*cos(t3)*cos(t4)+85=x; eq2=335*cos(t3)-260* sin(t3)*cos(t4)=y; eq3=0-335*sin(t2)* sin(t3) -77*cos(t2)...
8. ### Using logarithms in a geometric distribution question involving inequalities.

The question goes like this: It is know that 9% of the population belongs to blood group B. How many people must a doctor - who is sampling random people - examine to be 99.8% confident of finding at least one person with blood group B? P(X\geqx)\leq0.002 where X = the no. of people examined...
9. ### Finding Ratios and First Term of Geometric Sums

Three integers x, y, and z (where x <= y <= z) form a geometric series with a common ratio r (which is also an integer). Given x + y + z = 741, what is the sum of all possible values of z? (Ans Key: 4870) I started doing some guess and check with my calculator and got z values of 247, 513, and...
10. ### Geometric Sequence Problem

We are working with the explicit formulas for arithmetic AND geometric sequences. I get for the most part, but it is the world problems that stump me a little. Here's one that confused me that I could use help on: John buys a computer for 1200 dollars. He predicts that the value of the...
11. ### Geometric Sequence

2nd term=3 4th term=1/3 6th term= unknown, find. 3=ar 1/3=ar^3 Then that equals 9=r^2 r=3 6th term= ar^n-1 6th term=a(3)^5 6th term=a243 Where did I mess up at ?
12. ### Arithmetic and Geometric Sequences.

Hi, I just did these problems for my final review. Does anyone mind checking them? Tyvm. 1) Find the 98th term of an arithmetic sequence whose first three terms are 2,6,10 Ans: 390 2)Write the 21st term in arithmetic sequence with a first term of 7, and a common difference of 5. Ans: 107 3)...

I am also stuck on this question. Let {b sub k} be a geometric sequence. Given that (b sub 4)= 80, (b sub 9)=1280, and (S sub 9)=2555. Find the first term (b sub 1). I have tried it every way I know how but I am getting nowhere. No amount of searching on the internet has helped either...
14. ### Geometric Progression

Hi, I came across a GP questions as follows- The difference between 5th term and 3rd term of GP is 72. If the 1st term is 1. Find the common ratio. I had solved it. Please correct me. Where am I wrong? a= 1 as its the 1st term. ar^4 - ar^2 = 72. This implies r^4- r^2 = 72. From here I can...
15. ### Geometric Progression

The sum of an infinite GP is 16, its second term is 4. Find the first term
16. ### Convergence of a geometric power series centered at x = 2

2 Questions I have located at the bottom of the attached image.
17. ### Understanding Arithmetic and Geometric series, help?

Below are a few examples i pulled from by book, i was wondering if i could get some help with so i can have a better understanding on how to solve the rest. 8+3-2-7-12-....-87 1a) What Kind of series is this? Arithmetic, Geometric, or Neither? Why? 1b) Use the appropriate formula to find...
18. ### Geometric Sequences

How many terms of the geometric sequence 1.2, 2.4, 4.8, 9.6, 19.2...are required for the sum to be greater than 10,000? Do you use the equation sn=a(1-r^n)/1-r? And how is logarithms included in this question?
19. ### Infinite geometric series word problem

Q: A ball is dropped from a height of 32 ft. Each time it strikes the ground it rebounds 3/8ths of the distance from which it had fallen. Theoretically, how far will the ball travel before coming to a rest? Because the ball rebounds up then falls back down again before rebounding a next time, I...
20. ### Geometric Progression Word Problem

Q: The sum of the first and last terms of a G.P. of fourteen real terms is 7. The fifth term is the mean proportional between the second and last terms. Find the third term. All I have been able to come up with thus far are the equations: t1 + t14 = 7 and t2/t5 = t5/t14 Then I plugged in a...