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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`

A

`a_1=-10`

B

`a_2=-1`

C

`a_3 =-4`

D

`a_5 = +2`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`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):}}`
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