If an AP , a7=9 if a1 a2 a7 is least, the common difference is

Question

If an AP , a7=9 if a1 a2 a7 is least, the common difference is (A) (23/20) (B) (11/20) (C) (33/20) (D) (41/20)

Tardigrade Admin · Accepted Answer

Let d be the common difference ∴ a7=9 ∴ a1+6 d=9 Let D =a1 a2 a7=(9-6 d)(9-5 d) 9 =270 (d-(33/20))2-(9/400) For least value of D , d-(33/20)=0 ∴ d=(33/20)

Q. If an $A P, a_{7} = 9$ if $a_{1} a_{2} a_{7}$ is least, the common difference is

$\frac{23}{20}$

$\frac{11}{20}$

$\frac{33}{20}$

$\frac{41}{20}$

$\frac{13}{20}$

Let $d$ be the common difference
$∴ a_{7} = 9$
$∴ a_{1} + 6 d = 9$
Let $D = a_{1} a_{2} a_{7} = (9 - 6 d) (9 - 5 d) 9$
$= 270 {(d - \frac{33}{20})^{2} - \frac{9}{400}}$
For least value of $D, d - \frac{33}{20} = 0$
$∴ d = \frac{33}{20}$

Q. If an AP,a7​=9 if a1​a2​a7​ is least, the common difference is

2023​

2011​

2033​

2041​

2013​

Let d be the common difference ∴a7​=9 ∴a1​+6d=9 Let D=a1​a2​a7​=(9−6d)(9−5d)9 =270{(d−2033​)2−4009​} For least value of D,d−2033​=0 ∴d=2033​