If a1, a2, a3(a10) are three successive terms of a G.P. with common ratio r, the value of r for which a3 4 a2 3 a1 holds is given by

Question

If a1, a2, a3(a1>0) are three successive terms of a G.P. with common ratio r, the value of r for which a3 > 4 a2 3 a1 holds is given by (A) 1 < r < 3 (B) -3 < r < -1 (C) r > 3 or r < 1 (D) None of these

Tardigrade Admin · Accepted Answer

Let a1, a2, a3 be first three consecutive terms of G.P. with common ratio r . Then, a2=a1 r and a3=a1 r2 Now, a3>4 a2-3 a1 ⇒ a1 r2>4 a1 r-3 a1 ⇒ r2>4 r-3 ⇒ r2-4 r+3>0 ⇒ (r-1)(r-3)>0 ⇒ r<1 or r>3

Q. If $a_{1}, a_{2}, a_{3} (a_{1} > 0)$ are three successive terms of a $G . P$ . with common ratio $r$ , the value of $r$ for which $a_{3} > 4 a_{2}$ $3 a_{1}$ holds is given by

$1 < r < 3$

$- 3 < r < - 1$

$r > 3$ or $r < 1$

None of these

Q. If a1​,a2​,a3​(a1​>0) are three successive terms of a G.P. with common ratio r, the value of r for which a3​>4a2​ 3a1​ holds is given by

1<r<3

−3<r<−1

r>3 or r<1

None of these

Let a1​,a2​,a3​ be first three consecutive terms of G.P. with common ratio r. Then, a2​=a1​r and a3​=a1​r2 Now, a3​>4a2​−3a1​ ⇒a1​r2>4a1​r−3a1​ ⇒r2>4r−3 ⇒r2−4r+3>0 ⇒(r−1)(r−3)>0 ⇒r<1 or r>3

Q. If $a_{1}, a_{2}, a_{3} (a_{1} > 0)$ are three successive terms of a $G . P$ . with common ratio $r$ , the value of $r$ for which $a_{3} > 4 a_{2}$ $3 a_{1}$ holds is given by

$1 < r < 3$

$- 3 < r < - 1$

$r > 3$ or $r < 1$