Which term of the G.P `1/4, -1/2, 1, ...` is `-128`

Options

A. 9th
B. 10th
C. 11th
D. 12th

Answer

B

Explanation

Let the given series be
`(1)/(4),(-1)/(2),1,..........`
Let `a=(1)/(4)" and "r=-(1)/(2)xx(4)/(1)=-2`
`:." ""General term "=T_(n)=ar^(n-1)`
`implies-128=(1)/(4)(-2)^(n-1)`
`implies-512=(-2)^(n-1)`
`implies(-2)^(9)=(-2)^(n-1)`
`implies9=n-1impliesn=10`