If the second term of a G.P. is 9 and sum of the infinite terms is 40.5, then what will be the 3rd t

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05 Mar 2019 GP

If the second term of a G.P. is 9 and sum of the infinite terms is 40.5, then what will be the 3rd term?
Given that the first term is greater than 14.

OPtion

1) 4.5
2) 6
3) 7.5
4) 1.5
5) 1.0
6) 3.0
7) 3.5
8) 2.5
9) 0.333
10) None of these

Solution

nth term = a * r ^ (n-1)
=> For 2nd term => 9 = a*r^(2-1)
=> 9 = ar
=> r = 9/a

Sum of infinite terms in G.P = a/(1-r)

Sum of infinite terms in G.P => 40.5 = a/(1-r)
=> 40.5 - 40.5r = a
=> 40.5 = a + 40.5*9/a
=> 81a = 2a^2 + 729

Solving we get a = 27 or 13.5
As the first term is greater than 15, hence 13.5 is ruled out

So r = 9/27 = 1/3

Hence 3rd term => 27*(1/3)^(3-1) = 27*(1/3)^2 = 27/9 = 3

Correct Option: 6 Best Solution (7)

G.S.Kantharao   5 years AGO

a/1-r=ar/r(1-r)=81/2
18/r-r^2=81
1/r-r^2=9/2
9r^2-9r+2=0
9r^2-6r-3r+2=0
3r(3r-2)-1(3r-2)=0
(3r-1)(3r-2)=0
r=1/3 or 2/3
9*3=27,9,3 or
9*3/2=27/2,9,4...
As aq>14 then a3 =3
My option is 6👈

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AASHRAY AJAY SHARMA   5 years AGO

The second term in G.P is 9 i.e.,
a * r ^ (n-1) = 9 where 'n' is the second term(2)..
so we got ar = 9 ------ Equation (1)
Sum of infinite terms in G.P is 40.5 i.e.,
a/(1-r) = 40.5 ------- Equation(2)
From Equation (1) we got r = 2/a.
so substitute 'r' value in eq (2).. we got 'a' value = 27, r=1/3
third term = 27/9 = 3 (Option 6)

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Varun   5 years AGO

Let the numbers be 27 9 3
Then it satisfies
formula s_infinity = first_term/(1-common ratio)
Hence option (6)

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RAMADURAI NATESAN   5 years AGO

S(Infin) of G.P.=a/(1 - r ) where a is 1st term and r is common ratio , r lying between 0 and 1. Since a is 1st term and 9 is 2nd term, r = 9/a. S = a/(1 - 9/a)= a^2/(a - 9) = 40.5 (Given).Thus, a^2 - 40.5a + 364.5 = 0. Solving,roots are 13.5 and 27.0.Given that 1st term is greater than 14,we choose 27 as a ,the 1st term.2nd term being 9,
r = 1/3.Hence 3rd term is 3.

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Anji Babu Vanka   5 years AGO

solve the equation 40.5r^2-40.5r+9 you will get r=2/3 and 1/3
substitute to get value of a=27
Then ar^2 =27*(1/3)^2=3

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suryanarayana   5 years AGO

sum of infinite numbers is a/(1-r)= 40.5-------(1)
second term is ar=9--------(2)
from (1)&(2)
a=27 or 13.5 but first term is grater than 14
so. a=27
3rd term =ar²=(27)*(0.333)²=3

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Avinash   5 years AGO

a=27
r=1/3
second term=a*r^2=27*1/9=3

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