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kryton1212
 one year ago
a and b are +ve integers. a,4,b form a geometric sequence, and 4,b,a form an arithmetric sequence.
(a) Find the value of ab.
(b) Find the values of a and b.
(c) (i) Find the sum to infinity of the geometric sequence a,4,b,... .
(ii) Find the sum to infinity of all the terms that are +ve in the geometric sequence a,4,b.
kryton1212
 one year ago
a and b are +ve integers. a,4,b form a geometric sequence, and 4,b,a form an arithmetric sequence. (a) Find the value of ab. (b) Find the values of a and b. (c) (i) Find the sum to infinity of the geometric sequence a,4,b,... . (ii) Find the sum to infinity of all the terms that are +ve in the geometric sequence a,4,b.

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hartnn
 one year ago
Best ResponseYou've already chosen the best response.1if x,y,z form an geometric sequence, then \(y^2 =xz\) so, what about a,4 and b ?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1i can get you a simple explanation here... each next term of geometric sequence is MULTIPLIED by the common ratio 'r' so, in general, terms are a,ar,ar^2,ar^3..... when we have just 3 terms, we have a, ar, ar^2 for this (1st term * 3rd term) = (2nd term)^2 (you can check)

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1or in other words, they form a proportion, \(\dfrac{1st \: term}{2nd \: term}=\dfrac{2nd \: term}{3rd\: term}\)

hartnn
 one year ago
Best ResponseYou've already chosen the best response.116 is correct :) now if the terms are in arithmetic sequence, then 2* 2nd term = 1st term + 3rd term use this...

kryton1212
 one year ago
Best ResponseYou've already chosen the best response.1wow, i like the formulae

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1or if you don't want to remember the formula, you should know that difference between the terms is constant in arithmetic sequence so, difference between b and 4 = difference between a and b b  (4) = ab you'll get same equation :)

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1tell me what u get for a and b when you get it....2 equations, 2 unknowns...

kryton1212
 one year ago
Best ResponseYou've already chosen the best response.14+d=b b+d=a ar=4 ar^2=b are the equations correct?

kryton1212
 one year ago
Best ResponseYou've already chosen the best response.1i don't know, i just guess.....it's written couple of days ago. i forgot how...

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1forget about the 'd' and 'r' now we have 2 equations in a and b ab = 16 and from b(4) = ab, we have 2b =a4 you got these ? how..

kryton1212
 one year ago
Best ResponseYou've already chosen the best response.1uh, you said this moment ago. got it. a=8 , b=2

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1those values are correct. so b) is done right ? now c) part can you find the common ratio in 8,4,2,....?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1ohh! yes, r= 2 :) first term = a1 = 8 SUm to infinite is just \(\large \dfrac{a_1}{r1}\)

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1ohh....the r is not 2 :P

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1yes. r = 2nd term / 1st term = 3rd trm/ 2nd term =.... = 4/8 = 1/2

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1since r is LESS than 1, we use \(\huge S_\infty = \dfrac{a_1}{1r}\)

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1yes, there are 2 formula, depending on r less than 1 or greater than 1

kryton1212
 one year ago
Best ResponseYou've already chosen the best response.1i will remember. I just forgot at that moment..

kryton1212
 one year ago
Best ResponseYou've already chosen the best response.1i hate doing +ve / ve ....

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1remove all the negatives... 8,4,2,1,1/2 .... to 8,2,1/2 .... now whats the common ratio r =... ?

kryton1212
 one year ago
Best ResponseYou've already chosen the best response.1oh, i know what's the world happening! r=1/4

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1and since 1/4 is less than 1 you use a/ (1r)

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1\(\huge \color{red}\checkmark\)
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