hall & knight GP question

VITEEE 2015 Help › Algebra questions › hall & knight GP question

The first two terms of an infinite G. P. are together equal to 5,
and every term is 3 times the sum of all the terms that follow it; find
the series.

#Mathematics #Algebra

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6 Answers

262

Aditya Bhutra ·2011-04-01 00:17:22

let gp be --> a,ar,ar² ,..... âˆž
therefore T_n = ar^n-1 = arⁿ +arⁿ⁺¹ .... âˆž
for n=1, T₁= ar +ar² +...âˆž = ar1-r =a (first term of series)

therefore 2r=1 or r=1/2;

now from given info- a+ar=5;
or 3a/2=5
a=10/3

hence we can find the series!

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1

johncenaiit ·2011-04-01 00:28:01

i thought that the the 1st and 2nd terms are both equal to 5 !!!!

but i think you went wrong in the second step....
every term is 3 times the sum of all the terms that follow it

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1

mohit sengar ·2011-04-01 00:36:44

in the third step , it is

a = 3ar/1-r

so , r = 1/4
then a =4 and ar = 1 and so on...

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kunl ·2011-04-01 00:43:54

i m getting r=1/4
and a=4

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AKHIL ·2011-04-01 08:28:45

ya i think kunl is rite

coz a + ar = 5

then acc. to quesn

a = ar + ar² + ar³ .................

a =3 ar / 1-r

so that gives r = 1/4 and a=4...

so the series is 4 , 1 , 1/4................

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262

Aditya Bhutra ·2011-04-02 00:12:08

oh sorry.... i think i missed that '3'!!

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