Consider a decreasing G.P.: g 1, g 2, g 3, ldots ldots g n ldots . . . s such that g 1+ g 2+ g 3=13 and g 12+ g 22+ g 32=91 then which of the following does not hold?

Question

Consider a decreasing G.P.: g 1, g 2, g 3, ldots ldots g n ldots . . . s such that g 1+ g 2+ g 3=13 and g 12+ g 22+ g 32=91 then which of the following does not hold? (A) The greatest term of the G.P. is 9 . (B) 3 g4=g3 (C) g 1=1 (D) g 2=3

Tardigrade Admin · Accepted Answer

G.P.: ( a / r ), a , ar, a =3 and r =(1/3) or 3 (rejected) G.P. is 9,3,1, (1/3), ldots ldots . ⇒ C is not correct.

Q. Consider a decreasing G.P. : $g_{1}, g_{2}, g_{3}, \dots\dots g_{n} \dots ... s$ such that $g_{1} + g_{2} + g_{3} = 13$ and $g_{1}^{2} + g_{2}^{2} + g_{3}^{2} = 91$ then which of the following does not hold?

The greatest term of the G.P. is 9 .

$3 g_{4} = g_{3}$

$g_{1} = 1$

$g_{2} = 3$

G.P. : $\frac{a}{r}, a, a r$ ,
$a = 3$ and $r = \frac{1}{3}$ or 3 (rejected)
G.P. is $9, 3, 1, \frac{1}{3}, \dots\dots . \Rightarrow C$ is not correct.

Q. Consider a decreasing G.P. : g1​,g2​,g3​,……gn​…...s such that g1​+g2​+g3​=13 and g12​+g22​+g32​=91 then which of the following does not hold?

The greatest term of the G.P. is 9 .

3g4​=g3​

g1​=1

g2​=3

G.P. : ra​,a,ar, a=3 and r=31​ or 3 (rejected) G.P. is 9,3,1,31​,…….⇒C is not correct.

Q. Consider a decreasing G.P. : $g_{1}, g_{2}, g_{3}, \dots\dots g_{n} \dots ... s$ such that $g_{1} + g_{2} + g_{3} = 13$ and $g_{1}^{2} + g_{2}^{2} + g_{3}^{2} = 91$ then which of the following does not hold?

$3 g_{4} = g_{3}$

$g_{1} = 1$

$g_{2} = 3$

G.P. : $\frac{a}{r}, a, a r$ ,
$a = 3$ and $r = \frac{1}{3}$ or 3 (rejected)
G.P. is $9, 3, 1, \frac{1}{3}, \dots\dots . \Rightarrow C$ is not correct.