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

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

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

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

hartnn
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1i will remember. I just forgot at that moment..

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

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

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

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