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kryton1212
Group Title
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.
 one year ago
 one year ago
kryton1212 Group Title
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.
 one year ago
 one year ago

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kryton1212 Group TitleBest ResponseYou've already chosen the best response.1
@hartnn
 one year ago

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

kryton1212 Group TitleBest ResponseYou've already chosen the best response.1
ab=(4)^2=16 why?
 one year ago

kryton1212 Group TitleBest ResponseYou've already chosen the best response.1
it is also fixed?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
i 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)
 one year ago

kryton1212 Group TitleBest ResponseYou've already chosen the best response.1
okay, i understand
 one year ago

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

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

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

hartnn Group TitleBest ResponseYou've already chosen the best response.1
or 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 :)
 one year ago

kryton1212 Group TitleBest ResponseYou've already chosen the best response.1
yup, got it
 one year ago

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

kryton1212 Group TitleBest ResponseYou've already chosen the best response.1
4+d=b b+d=a ar=4 ar^2=b are the equations correct?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
ar = 4 ? how ?
 one year ago

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

hartnn Group TitleBest ResponseYou've already chosen the best response.1
forget 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..
 one year ago

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

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

hartnn Group TitleBest ResponseYou've already chosen the best response.1
b=2 was correct....
 one year ago

kryton1212 Group TitleBest ResponseYou've already chosen the best response.1
common ratio is 2
 one year ago

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

kryton1212 Group TitleBest ResponseYou've already chosen the best response.1
what? 8/3?
 one year ago

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

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

kryton1212 Group TitleBest ResponseYou've already chosen the best response.1
16/3 ...
 one year ago

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

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

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

hartnn Group TitleBest ResponseYou've already chosen the best response.1
try the last aprt ?
 one year ago

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

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

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

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

kryton1212 Group TitleBest ResponseYou've already chosen the best response.1
million thanks
 one year ago

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

hartnn Group TitleBest ResponseYou've already chosen the best response.1
welcome ^_^
 one year ago
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