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Let Sn(n ge 1) be a sequence of sets def...

Let `S_n(n ge 1)` be a sequence of sets defined by `S_1={0},S_2={3/2,5/2},S_4={15/4,19/4,23/4,27/4},.......`then

A

third element in `S_(20)` is `(439)/(20)`

B

third element in `S_(20)` is `(431)/(20)`

C

sum of the element in`S_(20)` is 589

D

sum of the element in`S_(20)` is 609

Text Solution

Verified by Experts

The correct Answer is:
A, C
`:.S_(1)={0}`
`S_(2)={(3)/(2),(5)/(2)}`
`S_(3)={(8)/(3),(11)/(3),(14)/(3)}`
`S_(4)={(15)/(4),(19)/(4),(23)/(4),(27)/(4)}`
Let `S=3+8+15+"......"+T_(19)`
`(ulS=ul3+ul8+"......"+ulT_(18)+ulT_(19))/(0=3+5+7+"......"+19" terms "-T_(19))`
`T_(19)=3+5+7+"......"+19" terms "`
`:.T_(19)=(19)/(2)(6+18xx2)=(19)/(2)xx42=399`
`S_(20)={(399)/(20),(419)/(20),(439)/(20)"....."}`
`:.` Third elements of `S_(20)=(439)/(20)`
Sum of elements of `S_(20)=(20)/(2)xx(1)/(2)[2xx399+19xx20]`
`=399+190=589`
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