If `2^(nd)` term of GP is 2 and the sum of infinite terms is 8 find the first term

Options

A. `8,2,(1)/(2),(1)/(8),......`
B. `10,2,(2)/(5),(2)/(25),......`
C. `4,2,1,(1)/(2),(1)/(2^(2)),......`
D. `6,3,(3)/(2),(3)/(4),......`

Answer

C

Explanation

Let the first term and common ratio of the G.P. is a and r respectively.
Then,`ar=2,(a)/(1-r)=8`
`implies(ar)/(r-r^(2))=8" "implies2=8r-8r^(2)`
`implies4r^(2)-4r+1=0" "impliesr=(1)/(2)`
`:.G.P. "is "4,2,1,(1)/(2),...`