Home
Class 12
MATHS
Let Sn(n leq 1) be a sequence of sets de...

Let `S_n(n leq 1)` be a sequence of sets defined by `S_1{0},S_2={3/2,5/2},S_3={15/4,19/4,23/4,27/4},.......`then

A

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

B

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

C

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

D

(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`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|24 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|10 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|30 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

For the S_(n)=3n^(2)+5n sequence, the number 5456 is the

Let a sequence {a_(n)} be defined by a_(n)=(1)/(n+1)+(1)/(n+2)+(1)/(n+3)+"...."+(1)/(3n) . Then:

If the set of natural numbers is partitioned into subsets S_1={1},S_2={2,3},S_3={4,5,6} and so on then find the sum of the terms in S_(50)dot

If S_n=cos^n theta+sin^n theta then find the value of 3S_4-2S_6

Find the sum of indicated number of terms of the following A.P.’s : 5, 2, -1, - 4, -7, ......., n terms.

Difference between S_N1 and S_N2 reaction ?

Given the sets A = {1, 3, 5), B = {2, 4, 6} and C = {0, 2, 4, 6, 8), which of the following may be considered as universal set (s) for all the three sets A, B and C (i) {0,1, 2, 3, 4, 5, 6} (ii) ϕ (iii) {0,1,2,3,4,5,6,7,8,9,10} (iv) {1,2,3,4,5,6,7,8}

Let k be an integer such that the triangle with vertices (k ,-3k),(5, k) and (-k ,2) has area 28s qdot units. Then the orthocentre of this triangle is at the point : (1) (1,-3/4) (2) (2,1/2) (3) (2,-1/2) (4) (1,3/4)

If S_1,S_2,S_3 be the sum of n, 2n, 3n terms of a G.P., show that : S_1(S_3-S_2)= (S_2-S_1)^2 .