Question

If an $AP , a_{7}=9$ if $a_{1} a_{2} a_{7}$ is least, the common difference is

• A. $\frac{23}{20}$
• B. $\frac{11}{20}$
• C. $\frac{33}{20}$
• D. $\frac{41}{20}$
• E. $\frac{13}{20}$

Answer 1

Answer: (C)

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