If 3 text rd , 6 text th and 10 text th terms of a non-constant A.P. are in G.P., then the common ratio of G.P. is

Question

If 3 text rd , 6 text th and 10 text th terms of a non-constant A.P. are in G.P., then the common ratio of G.P. is (A) (7/4) (B) (8/5) (C) (4/3) (D) 1

Tardigrade Admin · Accepted Answer

Let first term of A.P. be a and common difference be d, then

(a + 5 d)^{2} = (a + 2 d) (a + 9 d)

\Rightarrow a^{2} + 25 d^{2} + 10 a d = a^{2} + 11 a d + 18 d^{2}

\Rightarrow a d = 7 d^{2} \Rightarrow a = 7 d (∵ d \neq = 0)

∴ G.P. will be 9 d, 12 d, 16 d, \dots\dots ..

∴ Common difference = \frac{4}{3} .

Q. If $3^{rd}, 6^{th}$ and $1 0^{th}$ terms of a non-constant A.P. are in G.P., then the common ratio of G.P. is

$\frac{7}{4}$

$\frac{8}{5}$

$\frac{4}{3}$

1

Q. If 3rd ,6th and 10th terms of a non-constant A.P. are in G.P., then the common ratio of G.P. is

47​

58​

34​

1

Let first term of A.P. be a and common difference be d, then (a+5d)2=(a+2d)(a+9d) ⇒a2+25d2+10ad=a2+11ad+18d2 ⇒ad=7d2⇒a=7d(∵d=0) ∴ G.P. will be 9d,12d,16d,…….. ∴ Common difference =34​.

Q. If $3^{rd}, 6^{th}$ and $1 0^{th}$ terms of a non-constant A.P. are in G.P., then the common ratio of G.P. is

$\frac{7}{4}$

$\frac{8}{5}$

$\frac{4}{3}$