An infinite G.P. has first term as `a` and sum 5, then `a` belongs to a) `|a| < 10` b) `-10 < a < 0` c) `0 < a < 10` d) `a > 10`

Options

A. `xlt-10`
B. `-10ltxlt0`
C. `0ltxlt10`
D. `xgt0`

Answer

C

Explanation

Let r be the common ratio of the G.P. Then, `-1ltrlt1`.
Now,
Sum=5
`rArr" "(x)/(1-r)=5`
`rArr" "1-r=(x)/(5)`
`rArr" "r=1-(x)/(5)`
`rArr" "-1lt1-(x)/(5)lt" "[because-1ltrlt1]`
`rArr" "-2lt-(x)/(5)lt0rArr2gt(x)/(5)gt0rArr10gtxgt0rArrltxlt10`