# progressions

1. ### Geometric/arithmetic progressions in geometric trig

In triangle ABC, AB = BC, and BD is an altitude. Point E is on the extension of AC such that BE = 10. The values of tan<CBE, tan<DBE, and tan<ABE form a geometric progression, and the values of cot< DBE, cot< CBE, cot< DBC form an arithmetic progression. What is the area of triangle ABC?
2. ### summation of progressions

I have bunch of these kind of tasks at school but i dont know where to start. If someone here could show me how to complete tasks like that so i could do other tasks too. Prove that, 1x2+2x3+3x4+...+n(n+1)=n(n+1)(n+2) ------------...
3. ### Arithmetic and Geometric Progressions

Positive numbers a1, a2, a3 are in arithmetic progression, while positive numbers g1, g2, g3 are in geometric progression. Given that a1 + g1 = 26, a2 + g2 = 50, a3 + g3 = 114, and a1 + a2 + a3 = 60, find both progressions. ***Please note the 1, 2 and 3 are meant to be subscripts
4. ### Is there a way. Arithmetic Progressions. Again

I need help again. I'm stuck on something. If, in an Arithmetic Progression, U5 (5 term) =-.05 and the sum of the first 7 terms = 21, how can we find the first term?
5. ### progressions!

if a,b,c,d and p are distinct real numbers such that (a^2 +b^2 +c^2 )p^2 -2(ab + bc + cd)p+(b^2 + c^2 + d^2) is less than or equal to zero.. then prove thata,b,c,d are in geometric progression. thanks for you reply.
6. ### Geometric Progressions question help

A machine is required to have 5 speeds, lowest being 60 rev/min and the highest being 680 rev/min. state the complete range of speeds i) in AP and ii) in GP i have done the AP part, i am a little stuck with where to start with the GP part as i have the 1st and 5th terms of the sequence a...
7. ### Harmonical Progressions.....

If the mth term of a Harmonical Progression is n and the nth term is m then prove that the rth term is(mn)/r. Help Needed.............Thanks a lot in advance...
8. ### Arithmetic Progressions' Help Needed

I need help regarding the following question: Four different integers are in A.P. One of these integers is equal to the squares of the rest integers. Find the numbers. It is like this: If a, b, c, d are in A.P. then d=a^2 +b^2 +c^2 I know the answer, but I simply can't figure out the...
9. ### Stuck on progressions question

How many terms of the series 4,10,16, ....... must be taken such that the sum is equal to 602? So far i have: Sn=n/2(2a+(n-1)d) 602x2=n(2x4+(n-1)6) 1204=n(8+6n-6) 1204=8n+6n squared-6n 1204=6n squared+2n 602=3n squared+n n+3n squared -602=0 I have got my self into a bit of a pickle with...
10. ### Progressions

What are HP and GP. With examples please.
11. ### Geometric Progressions

Hello everyone. I'm working on the following problem: A geometric progression containing 20 terms has 48 as its fifth term. The ratio of the sum of its first 6 terms to that of its first 3 terms is 9:1. Find the sum of its last 5 terms. Here's what I've done with it so far: G.P. n = 20...
12. ### Arithmetic Progressions

Hi all. I'm working on the following problem: An arithmetic progression has 14 terms. The sum of the odd-numbered terms is 140 and the sum of the even-numbered terms is 161. Find the common difference of the progression and the 14th term. Here's what I've done with it so far... A.P. n = 14...
13. ### Geometric Progressions

Hi all. I'm trying to prove that ( 1 + x + x^2 + x^3 + ... + x^2k) ( 1 - x + x^2 - x^3 + ... + x^2k) = 1 + x^2 + x^4 + ... + x^4k, where k is a positive integer and x is not equal to -1, 1. This question was posted in the section on Geometric Progressions. I don't know how to begin with...
14. ### Progressions

If 1, log x (base y), log y (base z), -15 log z (base x) are in AP, then a) z^3 = x b) x = y^-1 c) z^-3 = y d) all of these Regards Sreedhar
15. ### Progressions

The sum of the first 3 terms of a geometric progression is 13 times its first term.Find the possible values of the common ratio of the geometric progression.
16. ### Progressions

please help me on how to solve this question For a geometric progression,the first term is 6 and the sum of the 3 terms is 126.Find a)the possible values of the common ratio b)the 6th term of the geometric progression.
17. ### Progressions and finding the sum of terms

Given this series (2,4,6,8,10,12...) the formula to find the sum of all numbers up to an nth term in the series is n(n+1). For example, the sum of numbers up to and including the 2nd term is 2(2+1)=6. But for this series (3,6,9,12,15...) what is the formula to find the sum of all numbers up to...
18. ### geometric progressions

(Cool) show that the sum of n terms of the series \log a + \log (2a) + \log (4a) + \log (8a) + .... is \log [a^{n} \, 2^{n(n-1)/2}]
19. ### Find max value - (Triangles, geometric progressions, greatest integer(floor)function)

If for r > 1, three successive terms of a Geometric Progression with common ratio r represent sides of a triangle, then find the maximum value of (\lfloor 2r \rfloor + \lfloor - r \rfloor)
20. ### Arccot series and Arithmetic progressions?

If x_1,x_2,x_3,\mbox{...} are in arithmetic progression with common difference d, show that: \mbox{arccot}\left(\frac{1 + x_{1}x_{2}}{d}\right) + \mbox{arccot}\left(\frac{1 + x_{2}x_{3}}{d}\right) + \mbox{arccot}\left(\frac{1 + x_{3}x_{4}}{d}\right) + \mbox{...} +\...