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If the sequence (a(n)) is in GP, such th...

If the sequence `(a_(n))` is in GP, such that `a_(4)//a_(6)=1//4 and a_(2)+a_(5)=216,` then `a_(1)` is equal to

A

12 or `(108)/(7)`

B

10

C

7 or `(54)/(7)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`because {a_(n)}` be a GP `" " therefore a_(1), a_(2), a_(3), a_(4),........, a_(n)` are in GP
`because (a_(4))/(a_(6))=(1)/(4) rArr (a_(1)r^(3))/(a_(1)r^(5))=(1)/(4) rArr r^(2)=4`
`therefore r= pm 2" " and a_(2)+a_(5)=216`
`a_(1)r+a_(1)r^(4)=216" " a_(1)(r+r^(4))=216`
For `r=2, a_(1)(2+16)=216 therefore a_(1)=12`
and for `r=-2, a_(1)(-2+16)=216 therefore a_(1)=(216)/(14)=(108)/(7)`
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