For an increasing A.P. `a_1, a_2, a_n ifa_1=a_2+a_3+a_5=-12` and `a_1a_3a_5=80 ,` then which of the following is/are true? `a_1=-10` b. `a_2=-1` c. `a_3=-4` d. `a_5=+2`

Options

A. `a_1=-10`
B. `a_2=-1`
C. `a_3 =-4`
D. `a_5 = +2`

Answer

A, C, D

Explanation

`a_(1),+a_(3)+a_(5)=-12`
`a+a+2d+a+4d=-12 (dgt0)`
a+2d=-4 (1)
`a_(1)a_(3)a_(5)=80`
`a(a+2d)(a+4d)=80`
or (-4-2d)(-4+2d)=-20 or d=`pm3`
Since A.P is increasing, so d = `pm3`, a=-10. Hence,
`{:(a_(1)=-10,a_(2)=-7),(a_(3)=a+2d=-10+6=-4),(a_(5)=a+4d=-10+12=2):}}`