Question

For an increasing AP $a_1,a_2,.....,a_n,$ if $a_1+a_2+a_3=-12$ and $a_1{a}_3{a}_5=80,$ then which of the following does not hold?

• A. $a_1=-10$
• B. $a_2=-1$
• C. $a_3=-4$
• D. $a_5=2$

Answer 1

Answer: (B)

$\because$ $a_1+a_3+a_5=-12$ $a+(a+2d)+(a+4d)=-12$ $(\because d>0)$ $\Rightarrow$ $a+2d=-4$ ...(i) and $a_1{a}_3{a}_5=80$ $\Rightarrow$ $a(a+2d)(a+4d)=80$ $\Rightarrow$ $a(-4)(-4-2d+4d)=80$ [from Eq. (i)] $\Rightarrow$ $(-4-2d)(-4)(-4-2d+4d)=80$ $\Rightarrow$ $4(4+2d)(-4+2d)=80$ $\Rightarrow$ $4(4d^2-16)=80$ $\Rightarrow$ $4d^2=16+20=36$ $\Rightarrow$ $d^2=9$ $\therefore$ $d=\pm 3$ Since, AP is increasing, then $d=+3;a=-10$ $\therefore$ $a_1=-10;a_2=-7$ $a_3=a+2d=-10+6=-4$ $a_5=a+4d=-10+8=-2$