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Let {a(n)} be a GP such that (a(4))/(...

Let `{a_(n)}` be a 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
`:.{a_n}` be a GP `" ":. a_1,a_2,a_3,a_4,"....",a_n` are in GP
`:. (a_4)/(a_6) = (1)/(4) implies (a_1 r^(3))/(a_1 r^(5)) =(1)/(4) implies r^(2) =4`
`:. r = pm 2 ` and `a_2 + a_5 = 216`
`a_1r + a_1r^(4) = 216 " "a_1(r + r^(4)) = 216`
For ` r=2, a_1 ( 2+ 16) = 216 " " :. a_1 =12`
and for `r= -2 ,a_1(-2 + 16) = 216 " " :. a_1 =(216)/(14)=(108)/(7)`
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